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Complex Number — NDA Mathematics PYQs

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

Complex Number — NDA Mathematics PYQs

Consider the following inequalities : I. 1+4i>3+2i II. 2+3i III. 4+3i>3+4i where i= -1 How many of the above are valid ?

If p , q , r are the cube roots of unity, then what is vmatrix p^2+q^2 & r^2 & r^2 p^2 & q^2+r^2 & p^2 q^2 & q^2 & r^2+p^2 vmatrix equal to ?

If , , are cube roots of -8 , then what is ^2 p^2+ ^2 q^2+ ^2 r^2 ^2 p^2+ ^2 q^2+ ^2 r^2 equal to ?

Let Z₁ and Z₂ be complex numbers such that 3Z₁ 4Z₂ is purely imaginary. What is | Z₁+Z₂ Z₁-Z₂ | equal to ?

If is a non-real cube root of unity, then what is a root of the following equation? vmatrix x+1 & & ^2 & x+ ^2 & 1 ^2 & 1 & x+ vmatrix = 0

If x + 1 x = 2 , then what is x^3 + 1 x^3 equal to?

If z 0 is a complex number, then what is amp (z) + amp ( z ) equal to?

If = -1 + -3 2 , then what is the value of (1 + ¹⁹ - ³⁵)¹⁰⁰ - (1 - 3 ²⁵ + ³⁸)⁵⁰ ?

What is ( 3 +i 3 -i )^3 equal to?

If ( 1-i 1+i )^ 2m ( 1+i 1-i )^ 2n = 1 , where i = -1 , then what is the smallest positive value of (m - n) ?

Let 1 , , ^2 be three cube roots of unity. If x = a + b , y = a + b ^2 , z = a ^2 + b , then what is x^2 + y^2 + z^2 equal to?

If 1 is a cube root of unity, then what is (1+ - ^2 )¹⁰⁰+ (1- + ^2 )¹⁰⁰ equal to?

What is the value of the sum _ n=1 ²⁰ (i^ n-1 +i^n+i^ n+1 ) where i= -1 ?

If =- 1 2 +i 3 2 then what is | array ccc 1+ & 1+ ^2 & + ^2 1 & & ^2 1 & 1 ^2 & 1 array | equal to?

If x, y and z are the cube roots of unity, then what is the value of x y+y z+z x ?

What is (1+i)^4+(1-i)^4 equal to, where i= -1 ?

If 1 is a cube root of unity, then what are the solution of (z-100)^3+1000=0 ?

Paragraph: Let Z₁ and Z₂ be any two complex numbers such that Z₁^2+Z₂^2+Z₁ Z₂=0 Question: What is the value of 1 2 + Re ( Z ₁ Z ₂ ) ?

If z is any complex number and i z^3+z^2-z+i=0 , where i= -1 , then what is the value of (|z|+1)^2 ?

Let z₁ and z₂ be two complex numbers such that | z₁+z₂ z₁-z₂ |=1 , then what is Re ( z₁ z₂ )+1 equal to?

Paragraph: Let Z₁ and Z₂ be any two complex numbers such that Z₁^2+Z₂^2+Z₁ Z₂=0 Question: What is the value of | Z₁ Z₂ | ?

What is the value of 12+5 i + 12-5 i , where i= -1 ?

If z z =|z+ z | , where z=x+i y, i= -1 then the locus of z is a pair of :

Which one of the following is a square root of - -1 ?

Consider equation-I: z^3+2 z^2+2 z+1=0 and equation -II: z¹⁹⁸⁵+z¹⁰⁰+1=0 Which of the following is a root of equation-I?

Consider equation-I: z^3+2 z^2+2 z+1=0 and equation -II: z¹⁹⁸⁵+z¹⁰⁰+1=0 What are the roots of equation – I?

Consider equation-I: z^3+2 z^2+2 z+1=0 and equation -II: z¹⁹⁸⁵+z¹⁰⁰+1=0 What is the number of common roots of equation-I and equation-II?

If is a non-real cube root of 1 , then what is the value of | 1- + ^2 | ?

If and are the distinct roots of equation x^2-x+1=0 , then what is the value of | ¹⁰⁰+ ¹⁰⁰ ¹⁰⁰- ¹⁰⁰ | ?

If z= 1+ i 3 1- i 3 where i= -1 , then what is the argument of z ?

If z is a complex number such that z-1 z+1 is purely imaginary, then what is |z| equal to?

Paragraph: Let z= 1+i 1-i where i= -1 Question: What is the modulus of z ?

What is the principal argument of 1 1+i where i= -1 ?

Paragraph: Let z= 1+i 1-i where i= -1 Question: What is angle such that z is purely imaginary? where n is an integer

What is the modulus of ( -3 2 - 1 2 )²⁰⁰ ?

If x^2+x+1=0 , then what is the value of x¹⁹⁹+x²⁰⁰+x²⁰¹ ?

What is _ n=1 ^ 8 n+7 i^n equal to, where i= -1 ?

Consider the following statements in respect of the roots of the equation x^3-8=0 : 1. The roots are non-collinear. 2. The roots lie on a circle of unit radius. Which of the above

Which one of the following is a square root of 2 a+2 a^2+b^2 , where a, b R ? where i= .

If z=x+i y , where i= -1 , then what does the equation z z +|z|^2+4(z+ z )-48=0 represent?

If i= -1 , then how many values does i^ -2 n have for different n Z ?

Consider the following in respect of a complex number Z : 1. (Z⁻¹ ) =( Z )⁻¹ 2. Z Z⁻¹=|Z|^2 Which of the above is/are correct?

The smallest positive integer n for which ( 1-i 1+i )^ n^2 where i= -1 , is

Consider the following statements in respect of an arbitrary complex number Z : 1. The difference of Z and its conjugate is an imaginary number. 2. The sum of Z and its conjugate i

If is a complex cube root of unity and x= ^2- -2 , then what is the value of x^2+4 x+7 ?

If x^2+y^2=1 , then what is 1+x+i y 1+x-i y equal to?