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Complex Number — JEE Main & Advanced Mathematics PYQs

551 previous year questions from Complex Number with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

551 questionsMathematicsSolutions on every page
1

The number of values of z C , satisfying the equations |z-(4+8i)|= 10 and |z-(3+5i)|+|z-(5+11i)|=4 5 , is:

JEE Main 2026 Solution View → 2

Let S = z C : z^2 + 6 ,iz - 3 = 0 . Then _ z S z^8 is equal to :

JEE Main 2026 Solution View → 3

Let the set of all values of k R such that the equation z( z + 2 + i) + k(2 + 3i) = 0 , z C , has at least one solution, be the interval [ , ] . Then 9( + ) is equal to:

JEE Main 2026 Solution View → 4

Let z₁, z₂ C be the distinct solutions of the equation z^2 + 4z - (1 + 12i) = 0 . Then |z₁|^2 + |z₂|^2 is equal to :

JEE Main 2026 Solution View → 5

Let S= z C : z^2+4z+16=0 . Then _ z S |z+ 3 i|^2 is equal to:

JEE Main 2026 Solution View → 6

Let z be a complex number such that |z+2| = |z-2| and ( z+3 z-i ) = 4 . Then |z|^2 is equal to:

JEE Main 2026 Solution View → 7

Let the circles C₁ : |z| = r and C₂ : |z - 3 - 4i| = 5 , z C , be such that C₂ lies within C₁ . If z₁ moves on C₁ , z₂ moves on C₂ and |z₁ - z₂| = 2 , then |z₁ - z₂| is equal to:

JEE Main 2026 Solution View → 8

Let x and y be real numbers such that 50 ( 2x 1+3i - y 1-2i ) = 31 + 17i , i = -1 . Then the value of 10(x - 3y) is :

JEE Main 2026 Solution View → 9

Let A= z C :|z-2| 4 and B= z C :|z-2|+|z+2|=5 . Then the max |z₁-z₂ |: z₁ ~A . and .z₂ ~B is :

JEE Main 2026 Solution View → 10

Let z be a complex number such that |z-6|=5 and |z+2-6 i|=5 . Then the value of z³+3 z²-15 z+141 is equal to

JEE Main 2026 Solution View → 11

Let z=(1+i)(1+2 i)(1+3 i) (1+n i) , where i= -1 . If |z|²=44200 , then n is equal to _ _ _ _

JEE Main 2026 Solution View → 12

If z= 3 2 + i 2 , i= -1 , then (z²⁰¹-i )⁸ is equal to

JEE Main 2026 Solution View → 13

Let S= z: 3 |2 z-3(1+i)| 7 be a set of complex numbers. Then _ z S | (z+ 1 2 (5+3 i) ) | is equal to :

JEE Main 2026 Solution View → 14

Let S= z C : 4 z²+ z =0 . Then _ z S |z|² is equal to:

JEE Main 2026 Solution View → 15

Let = -1+i 3 2 and = -1-i 3 2 , i= -1 . If (7-7 +9 )²⁰+(9+7 -7 )²⁰+(-7+9 +7 )²⁰+(14+7 +7 )²⁰=m¹⁰ , then m is _ _ _ _ _

JEE Main 2026 Solution View → 16

Let z be the complex number satisfying |z-5| 3 and having maximum positive principal argument. Then 34 | 5 z-12 5 i z+16 |² is equal to :

JEE Main 2026 Solution View → 17

If x²+x+1=0 , then the value of (x+ 1 x )⁴+ (x²+ 1 x² )⁴+ (x³+ 1 x³ )⁴+ + (x²⁵+ 1 x²⁵ )⁴ is:

JEE Main 2026 Solution View → 18

Let R denote the set of all real numbers. Let z₁=1+2 i and z₂=3 i be two complex numbers, where i= -1 . Let S= (x, y) R R : |x+i y-z₁ |=2 |x+i y-z₂ | . Then which of the following

JEE Advanced 2025 Solution View → 19

For a non-zero complex number z , let (z) denote the principal argument of z , with - < (z) . Let be the cube root of unity for which 0 < ( ) < . Let = ( _ n=1 ²⁰²⁵(- )^n ) . Then

JEE Advanced 2025 Solution View → 20

Let A = [0,2 ]: 1+10 Re ( 2 +i -3 i )=0 . Then _ A ^2 is equal to

JEE Main 2025 Solution View → 21

If the locus of z C , such that Re ( z-1 2 z+ i )+ Re ( z -1 2 z - i )=2 is a circle of radius r and center (a, b) then 15 a b r^2 is equal to :

JEE Main 2025 Solution View → 22

Among the statements (S1) : The set z C - - i :| z |=1 . and z - i z + i is purely real contains exactly two elements, and (S2) : The set z C - -1 :| z |=1 . and z -1 z +1 is purel

JEE Main 2025 Solution View → 23

Let the product of ₁=(8+i) +(7+4 i) and ₂=(1+8 i) +(4+7 i) be +i , i = -1 . Let p and q be the maximum and the minimum values of + respectively.

JEE Main 2025 Solution View → 24

If is a root of the equation x^2+x+1=0 and _ k =1 ^ n ( ^ k + 1 ^ k )^2=20 , then n is equal to

JEE Main 2025 Solution View → 25

Let A= z C:|z-2-i|=3 , B= z C: Re (z-i z)=2 and S=A B . Then _ z S |z|^2 is equal to ________ .

JEE Main 2025 Solution View → 26

If z₁, z₂, z₃ C are the vertices of an equilateral triangle, whose centroid is z ₀ , then _ k =1 ^3 ( z _ k - z ₀ )^2 is equal to

JEE Main 2025 Solution View → 27

Let z C be such that z^2+3 i z-2+i =2+3 i . Then the sum of all possible values of z^2 is

JEE Main 2025 Solution View → 28

Let z be a complex number such that |z|=1 . If 2+ k ^2 z k + z = kz , k R , then the maximum distance of k + ik ^2 from the circle | z -(1+2 i )|=1 is:

JEE Main 2025 Solution View → 29

Let integers a , b [-3,3] be such that a + b 0 . Then the number of all possible ordered pairs (a, b), for which | z- a z+ b |=1 and | array ccc z+1 & & ^2 & z+ ^2 & 1 ^2 & 1 & z+

JEE Main 2025 Solution View → 30

Let ( |z₁-8-2 i | 1 ) and ( |z₂-2+6 i | 2, z₁, z₂ C ). Then the minimum value of ( |z₁-z₂ | ) is :

JEE Main 2025 Solution View → 31

If +i and +i are the roots of x^2-(3-2 i) x-(2 i-2)=0, i= -1 , then + is equal to :

JEE Main 2025 Solution View → 32

Let O be the origin, the point A be z₁= 3 +2 2 i , the point B (z₂ ) be such that 3 |z₂ |= |z₁ | and (z₂ )= (z₁ )+ 6 . Then

JEE Main 2025 Solution View → 33

If and are the roots of the equation 2 z^2-3 z-2 i =0 , where i = -1 , then 16 Re ( ¹⁹+ ¹⁹+ ¹¹+ ¹¹ ¹⁵+ ¹⁵ ) lm ( ¹⁹+ ¹⁹+ ¹¹+ ¹¹ ¹⁵+ ¹⁵ ) is equal to

JEE Main 2025 Solution View → 34

The number of complex numbers z , satisfying |z|=1 and | z z + z z |=1 , is :

JEE Main 2025 Solution View → 35

Let , be the roots of the equation x^2-a x-b=0 with Im ( ) Im ( ) . Let P_n= ^n- ^n . If P ₃=-5 7 i, P ₄=-3 7 i, P ₅=11 7 i and P ₆=45 7 i , then | ^4+ ^4 | is equal to .

JEE Main 2025 Solution View → 36

Let | z -i 2 z +i |= 1 3 , z C , be the equation of a circle with center at C . If the area of the triangle, whose vertices are at the points (0,0), C and ( , 0) is 11 square units

JEE Main 2025 Solution View → 37

Let the curve z(1+i)+ z (1-i)=4, z C , divide the region |z-3| 1 into two parts of areas and . Then | - | equals :

JEE Main 2025 Solution View → 38

Let z₁, z₂ and z₃ be three complex numbers on the circle |z|=1 with (z₁ )= - 4 , (z₂ )=0 and (z₃ )= 4 . If |z₁ z ₂+z₂ z ₃+z₃ z ₁ |^2= + 2 , , Z , then the value of ^2+ ^2 is :

JEE Main 2025 Solution View → 39

Let S= a+b 2 : a, b Z , T₁= (-1+ 2 )^n: n N , and T₂= (1+ 2 )^n: n N . Then which of the following statements is (are) TRUE?

JEE Advanced 2024 Solution View → 40

Let z be a complex number such that the real part of z-2 i z+2 i is zero. Then, the maximum value of |z-(6+8 i)| is equal to

JEE Main 2024 Solution View → 41

The sum of the square of the modulus of the elements in the set z= a + ib : a , b Z , z C ,|z-1| 1,|z-5| |z-5 i | is ________

JEE Main 2024 Solution View → 42

The sum of all possible values of [- , 2 ] , for which 1+i 1-2 i is purely imaginary, is equal

JEE Main 2024 Solution View → 43

Let z be a complex number such that |z+2|=1 and Im ( z+1 z+2 )= 1 5 . Then the value of | Re ( z+2 )| is

JEE Main 2024 Solution View → 44

If z₁, z₂ are two distinct complex number such that | z₁-2 z₂ 1 2 -z₁ z ₂ |=2 , then

JEE Main 2024 Solution View → 45

Let S₁= z C:|z| 5 , S₂= z C: Im ( z+1- 3 i 1- 3 i ) 0 and S₃= z C: Re (z) 0 . Then the area of the region S₁ S₂ S₃ is :

JEE Main 2024 Solution View → 46

Consider the following two statements : Statement I : For any two non-zero complex numbers z₁, z₂ , ( |z₁ |+ |z₂ | ) | z₁ |z₁ | + z₂ |z₂ | | 2 ( |z₁ |+ |z₂ | ) , and Statement II :

JEE Main 2024 Solution View → 47

The area (in sq. units) of the region S= z C :|z-1| 2 ;(z+ z )+i(z- z ) 2, Im (z) 0 is

JEE Main 2024 Solution View → 48

Let and be the sum and the product of all the non-zero solutions of the equation ( z )^2+|z|=0 , z C. Then 4 ( ^2+ ^2 ) is equal to :

JEE Main 2024 Solution View → 49

If z is a complex number such that z ≤ 1 , then the minimum value of z + 1 2 3 + 4 i is:

JEE Main 2024 Solution View → 50

Let P = z ∈ ℂ : z + 2 − 3 i ≤ 1 and Q = z ∈ ℂ : z 1 + i + z ¯ 1 − i ≤ − 8 . Let in P ∩ Q , z − 3 + 2 i be maximum and minimum at z 1 and z 2 respectively. If z 1 2 + 2 z 2 = α + β

JEE Main 2024 Solution View → 51

Let S = z ∈ C : z − 1 = 1 and 2 − 1 z + z ¯ - i z - z ¯ = 2 2 . Let z 1 , z 2 ∈ S be such that z 1 = max z ∈ s z and z 2 = min z ∈ s z . Then 2 z 1 − z 2 2 equals:

JEE Main 2024 Solution View → 52

Let z 1 and z 2 be two complex number such that z 1 + z 2 = 5 and z 1 3 + z 2 3 = 20 + 15 i . Then z 1 4 + z 2 4 equals-

JEE Main 2024 Solution View → 53

If α denotes the number of solutions of 1 − i x = 2 x and β = z arg z , where z = π 4 1 + i 4 1 − π · i π + i + π − i 1 + π · i , i = − 1 , then the distance of the point α , β fro

JEE Main 2024 Solution View → 54

If z is a complex number, then the number of common roots of the equation z 1985 + z 100 + 1 = 0 and z 3 + 2 z 2 + 2 z + 1 = 0 , is equal to :

JEE Main 2024 Solution View → 55

If z = x + i y , x y ≠ 0 , satisfies the equation z 2 + i z ¯ = 0 , then z 2 is equal to :

JEE Main 2024 Solution View → 56

Let r and θ respectively be the modulus and amplitude of the complex number z = 2 - i 2 tan 5 π 8 , then ( r , θ ) is equal to

JEE Main 2024 Solution View → 57

Let α , β be the roots of the equation x 2 - 6 x + 3 = 0 such that Im ( α ) > Im ( β ) . Let a , b be integers not divisible by 3 and n be a natural number such that α 99 β + α 98

JEE Main 2024 Solution View → 58

If z = 1 2 - 2 i , is such that | z + 1 | = α z + β ( 1 + i ) , i = - 1 and α , β ∈ R , then α + β is equal to

JEE Main 2024 Solution View → 59

Let α , β be the roots of the equation x 2 - x + 2 = 0 with Im ( α ) > Im ( β ) . Then α 6 + α 4 + β 4 - 5 α 2 is equal to

JEE Main 2024 Solution View → 60

Let the complex numbers α and 1 α ¯ lie on the circles z - z 0 2 = 4 and z - z 0 2 = 16 respectively, where z 0 = 1 + i . Then, the value of 100 | α | 2 is__________.

JEE Main 2024 Solution View → 61

If S = z ∈ C : | z - i | = | z + i | = | z - 1 | , then, n ( S ) is:

JEE Main 2024 Solution View → 62

If α satisfies the equation x 2 + x + 1 = 0 and ( 1 + α ) 7 = A + B α + C α 2 , A , B , C ≥ 0 , then 5 ( 3 A - 2 B - C ) is equal to

JEE Main 2024 Solution View → 63

Let A 1 , A 2 , A 3 , &#8230; , A 8 be the vertices of a regular octagon that lie on a circle of radius 2 . Let P be a point on the circle and let P A i denote the distance between

JEE Advanced 2023 Solution View → 64

Let A = 1967 + 1686 i sin &#952; 7 - 3 i cos &#952; : &#952; &#8712; R . If A contains exactly one positive integer n , then the value of n is

JEE Advanced 2023 Solution View → 65

Let z be a complex number satisfying z 3 + 2 z 2 + 4 z &#175; - 8 = 0 , where z &#175; denotes the complex conjugate of z . Let the imaginary part of z be nonzero. Match each entry

JEE Advanced 2023 Solution View → 66

If the set Re z - z &#175; + z z &#175; 2 - 3 z + 5 z &#175; : z &#8712; &#8450; , Re z = 3 is equal to the interval ( &#945; , &#946; ] , then 24 &#946; - &#945; is equal to

JEE Main 2023 Solution View → 67

Let S = z &#8712; &#8450; : z &#175; = i z 2 + Re ( z &#175; ) . Then &#8721; z &#8712; S | z | 2 is equal to

JEE Main 2023 Solution View → 68

Let w = z z &#175; + k 1 z + k 2 i z + &#955; ( 1 + i ) , k 1 , k 2 &#8712; &#8477; . . Let R e ( w ) = 0 be the circle C of radius 1 in the first quadrant touching the line y = 1

JEE Main 2023 Solution View → 69

Let C be the circle in the complex plane with centre z 0 = 1 2 1 + 3 i and radius r = 1 . Let z 1 = 1 + i and the complex number z 2 be outside circle C such that z 1 - z 0 z 2 - z

JEE Main 2023 Solution View → 70

For a &#8712; &#8450; , let A = z &#8712; &#8450; : Re ( a + z &#175; ) &#62; Im ( a &#175; + z ) and B = z &#8712; &#8450; : Re ( a + z &#175; ) &#60; Im ( a &#175; + z ) . Then a

JEE Main 2023 Solution View → 71

Let S = z &#8712; &#8450; - i , 2 i : z 2 + 8 i z - 15 z 2 - 3 i z - 2 &#8712; &#8477; . &#945; - 13 11 i &#8712; S , &#945; &#8712; &#8477; - 0 , then 242 &#945; 2 is equal to

JEE Main 2023 Solution View → 72

Let w 1 be the point obtained by the rotation of z 1 = 5 + 4 i about the origin through a right angle in the anticlockwise direction, and w 2 be the point obtained by the rotation

JEE Main 2023 Solution View → 73

Let S = z = x + i y : 2 z - 3 i 4 z + 2 i is a real number . Then which of the following is NOT correct?

JEE Main 2023 Solution View → 74

Let the complex number z = x + i y be such that 2 z - 3 i 2 z + i is purely imaginary. If x + y 2 = 0 , then y 4 + y 2 - y is equal to

JEE Main 2023 Solution View → 75

Let A = &#952; &#8712; 0 , 2 &#960; : 1 + 2 i sin &#952; 1 - i sin &#952; is purely imaginary Then the sum of the elements is in A is

JEE Main 2023 Solution View → 76

If for z = &#945; + i &#946; , z + 2 = z + 4 ( 1 + i ) , then &#945; + &#946; and &#945; &#946; are the roots of the equation

JEE Main 2023 Solution View → 77

Let a &#8800; b be two non-zero real numbers. Then the number of elements in the set X = z &#8712; C : Re a z 2 + b z = a and Re b z 2 + a z = b is equal to

JEE Main 2023 Solution View → 78

For &#945; , &#946; , z &#8712; &#8450; and &#955; &#62; 1 , if &#955; - 1 is the radius of the circle z - &#945; 2 + z - &#946; 2 = 2 &#955; , then &#945; - &#946; is equal to ___

JEE Main 2023 Solution View → 79

Let a , b be two real numbers such that a b &#60; 0 . If the complex number 1 + a i b + i is of unit modulus and a + i b lies on the circle z - 1 = 2 z , then a possible value of 1

JEE Main 2023 Solution View → 80

If the center and radius of the circle z - 2 z - 3 = 2 are respectively &#945; , &#946; and &#947; , then 3 &#945; + &#946; + &#947; is equal to

JEE Main 2023 Solution View → 81

The complex number z = i - 1 cos &#960; 3 + i sin &#960; 3 is equal to:

JEE Main 2023 Solution View → 82

For all z &#8712; C on the curve C 1 : | z | = 4 , let the locus of the point z + 1 z be the curve C 2 . Then

JEE Main 2023 Solution View → 83

Let z = 1 + i and z 1 = 1 + i z &#175; z &#175; ( 1 - z ) + 1 z &#183; Then 12 &#960; arg z 1 is equal to

JEE Main 2023 Solution View → 84

Let &#945; = 8 - 14 i , A = z &#8712; &#8450; : &#945; z - &#945; &#175; z &#175; z 2 - ( z &#175; ) 2 - 112 i = 1 and B = z &#8712; &#8450; : z + 3 i = 4 Then, &#8721; z &#8712; A

JEE Main 2023 Solution View → 85

For two non-zero complex number z 1 and z 2 , if Re z 1 z 2 = 0 and Re z 1 + z 2 = 0 , then which of the following are possible? (A) Im z 1 &#62; 0 and Im z 2 &#62; 0 (B) Im z 1 &#

JEE Main 2023 Solution View → 86

Let z be a complex number such that z - 2 i z + i = 2 , z &#8800; - i . Then z lies on the circle of radius 2 and centre

JEE Main 2023 Solution View → 87

Let z 1 = 2 + 3 i and z 2 = 3 + 4 i . The set S = z &#8712; C : z - z 1 2 - z - z 2 2 = z 1 - z 2 2 represents a

JEE Main 2023 Solution View → 88

The value of 1 + sin 2 &#960; 9 + i cos 2 &#960; 9 1 + sin 2 &#960; 9 - i cos 2 &#960; 9 3 is

JEE Main 2023 Solution View → 89

Let p , q &#8712; &#8477; and ( 1 - 3 i ) 200 = 2 199 ( p + i q ) , i = - 1 . Then, p + q + q 2 and p - q + q 2 are roots of the equation.

JEE Main 2023 Solution View → 90

Let z &#175; denote the complex conjugate of a complex number z . If z is a non-zero complex number for which both real and imaginary parts of z &#175; 2 + 1 z 2 are integers, then

JEE Advanced 2022 Solution View → 91

Let z be a complex number with non-zero imaginary part. If 2 + 3 z + 4 z 2 2 - 3 z + 4 z 2 is a real number, then the value of z 2 is ______.

JEE Advanced 2022 Solution View → 92

Let z &#175; denote the complex conjugate of a complex number z and let i = - 1 . In the set of complex numbers, the number of distinct roots of the equation z &#175; - z 2 = i z &

JEE Advanced 2022 Solution View → 93

If z &#8800; 0 be a complex number such that z - 1 z = 2 , then the maximum value of z is

JEE Main 2022 Solution View → 94

Let S = z = x + i y : z - 1 + i &#8805; z , z &#60; 2 , z + i = z - 1 . Then the set of all values of x , for which w = 2 x + i y &#8712; S for some y &#8712; &#8477; , is

JEE Main 2022 Solution View → 95

If z = 2 + 3 i , then z 5 + z &#175; 5 is equal to:

JEE Main 2022 Solution View → 96

Let z = a + i b , b &#8800; 0 be complex numbers satisfying z 2 = z &#175; &#183; 2 1 - z . Then the least value of n &#8712; N , such that z n = z + 1 n , is equal to _____ .

JEE Main 2022 Solution View → 97

Let S 1 = z 1 &#8712; C : z 1 - 3 = 1 2 and S 2 = z 2 &#8712; C : z 2 - z 2 + 1 = z 2 + z 2 - 1 . Then, for z 1 &#8712; S 1 and z 2 &#8712; S 2 , the least value of z 2 - z 1 is

JEE Main 2022 Solution View → 98

Let S be the set of all &#945; , &#946; , &#960; &#60; &#945; , &#946; &#60; 2 &#960; , for which the complex number 1 - i sin &#945; 1 + 2 i sin &#945; is purely imaginary and 1 +

JEE Main 2022 Solution View → 99

Let the minimum value v 0 of v = z 2 + z - 3 2 + z - 6 i 2 , z &#8712; &#8450; is attained at z = z 0 . Then 2 z 0 2 - z &#175; 0 3 + 3 2 + v 0 2 is equal to

JEE Main 2022 Solution View → 100

Let S = z &#8712; &#8450; : z 2 + z &#175; = 0 . Then &#8721; z &#8712; S Re z + Im z is equal to _______.

JEE Main 2022 Solution View → 101

If z = x + i y satisfies z - 2 = 0 and z - i - z + 5 i = 0 , then

JEE Main 2022 Solution View → 102

Let O be the origin and A be the point z 1 = 1 + 2 i . If B is the point z 2 , Re z 2 &#60; 0 , such that O A B is a right angled isosceles triangle with O B as hypotenuse, then wh

JEE Main 2022 Solution View → 103

For z &#8712; &#8450; if the minimum value of z - 3 2 + z - p 2 i is 5 2 , then a value of p is _______.

JEE Main 2022 Solution View → 104

If &#945; , &#946; , &#947; , &#948; are the roots of the equation x 4 + x 3 + x 2 + x + 1 = 0 , then &#945; 2021 + &#946; 2021 + &#947; 2021 + &#948; 2021 is equal to

JEE Main 2022 Solution View → 105

For n &#8712; N , let S n = z &#8712; C : z - 3 + 2 i = n 4 and T n = z &#8712; C : z - 2 + 3 i = 1 n . Then the number of elements in the set n &#8712; N : S n &#8745; T n = &#981

JEE Main 2022 Solution View → 106

Let z represent the principal argument of the complex number z . The, z = 3 and arg z - 1 - arg z + 1 = &#960; 4 intersect:

JEE Main 2022 Solution View → 107

Let &#945; and &#946; be the roots of the equation x 2 + 2 i - 1 = 0 . Then, the value of &#945; 8 + &#946; 8 is equal to

JEE Main 2022 Solution View → 108

Let S = z &#8712; C : z - 2 &#8804; 1 , z 1 + i + z &#175; 1 - i &#8804; 2 . Let z - 4 i attains minimum and maximum values, respectively, at z 1 &#8712; S and z 2 &#8712; S . If 5

JEE Main 2022 Solution View → 109

Sum of squares of modulus of all the complex numbers z satisfying z &#175; = i z 2 + z 2 - z is equal to

JEE Main 2022 Solution View → 110

The number of elements in the set z = a + i b &#8712; &#8450; : a , b &#8712; &#8484; and 1 &#60; z - 3 + 2 i &#60; 4 is _____.

JEE Main 2022 Solution View → 111

The number of points of intersection z - 4 + 3 i | = 2 and z + z - 4 = 6 , z &#8712; C is

JEE Main 2022 Solution View → 112

Let for some real numbers &#945; and &#946; , a = &#945; - i &#946; . If the system of equations 4 i x + 1 + i y = 0 and 8 cos 2 &#960; 3 + i sin 2 &#960; 3 x + a &#175; y = 0 has

JEE Main 2022 Solution View → 113

The area of the polygon, whose vertices are the non-real roots of the equation z &#175; = i z 2 is

JEE Main 2022 Solution View → 114

If z 2 + z + 1 = 0 , z &#8712; C , then &#8721; n = 1 15 z n + ( - 1 ) a 1 z n 2 is equal to _____.

JEE Main 2022 Solution View → 115

Let A = z &#8712; C : z + 1 z - 1 &#60; 1 and B = z &#8712; C : arg z - 1 z + 1 = 2 &#960; 3 . Then A &#8745; B is

JEE Main 2022 Solution View → 116

Let z 1 and z 2 be two complex numbers such that z &#175; 1 = i z &#175; 2 and arg z 1 z &#175; 2 = &#960; , then the argument of z 1 is

JEE Main 2022 Solution View → 117

Let a circle C in complex plane pass through the points z 1 = 3 + 4 i , z 2 = 4 + 3 i and z 3 = 5 i . If z &#8800; z 1 is a point on C such that the line through z and z 1 is perpe

JEE Main 2022 Solution View → 118

Let S = z &#8712; &#8450; : z - 3 &#8804; 1 and z 4 + 3 i + z &#175; 4 - 3 i &#8804; 24 . If &#945; + i &#946; is the point in S which is closest to 4 i , then 25 &#945; + &#946; i

JEE Main 2022 Solution View → 119

Let A = z &#8712; C : 1 &#10877; z - 1 + i &#10877; 2 and B = z &#8712; A : z - 1 - i = 1 . Then, B

JEE Main 2022 Solution View → 120

Let &#952; 1 , &#952; 2 , &#8230; , &#952; 10 be positive valued angles (in radian) such that &#952; 1 + &#952; 2 + &#8943; + &#952; 10 = 2 &#960; . Define the complex numbers z 1

JEE Advanced 2021 Solution View →
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