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Complex Number — BITSAT Mathematics PYQs

30 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 — BITSAT Mathematics PYQs

The points represented by the complex number 1+i,-2+3 i, 5 3 i on the argand plane are

The modulus of the complex number z such that |z+3-i|=1 and (z)= is equal to

If z, z ,-z,- z forms a rectangle of area 2 3 square units, then one such z is

If z₁, z₂, . . z_n are complex numbers such that |z₁ |= |z₂ |= . .= |z_n |=1 , then |z₁+z₂+ . .+z_n | is equal to

If |z₁ |=2, |z₂ |=3, |z₃ |=4 and |2 z₁+3 z₂+4 z₃ |= 4 , then absolute value of 8 z₂ z₃+27 z₃ z₁+64 z₁ z₂ equals

The modulus of (1+i 3 )(2+2 i) ( 3 -i) is

i⁵⁷+ 1 i²⁵ , when simplified has the value

If |w|=2 , then the set of points z=w- 1 w is contained in or equal to the set of points z satisfying

The smallest positive integral value of n such that [ 1+ 8 +i 8 1+ 8 -i 8 ]^n is purely imaginary, is equal to

If z is a complex number such that z²=( z )² , then

If z₁= 2 [ 4 +i 4 ] and z₂= 3 [ 3 +i 3 ] then |z₁ z₂ | is equal to m . Value of m is

If |z₁ |= |z₂ |= . . |z_ n |=1, then the value of |z₁+z₂+ . z_ n |- | 1 z₁ + 1 z₂ + .+ 1 z_ n | is,

The value of &#955; for which the loci arg z = &#960; 6 and | z - 2 3 i | = &#955; on the argand plane touch each other is

If z 1 and z &#175; 1 represents adjacent vertices of a regular polygon of n sides and if I m z 1 R e z 1 = 2 - 1 , then n is equal to

The n th roots of unity are in

If z = a + i b satisfies arg ( z - 1 ) = arg ( z + 3 i ) , then ( a - 1 ) : b =

If z 1 , z 2 and z 3 represent the vertices of an equilateral triangle such that z 1 = z 2 = z 3 then

If z₁= 3 +i 3 and z₂= 3 +i , then the complex number ( z ₁ z ₂ )⁵⁰ lies in the :

The root of the equation 2(1+i) x²-4(2-i) x-5-3 i=0 which has greater modulus is

If complex number z₁, z₂ and 0 are vertices of equilateral triangle, then z₁²+z₂²-z₁ z₂ is equal to

If z=x+i y, z^ 1 / 3 =a-i b, then x a - y b =k (a²-b² ) where k is equal to

i⁵⁷+ 1 i²⁵ , when simplified has the value

The complex number z=z+i y which satisfies the equation | z-3 i z+3 i |=1, lies on

If the real part of z +2 z -1 is 4, z 1, then the locus of the point representing z in the complex plane is

If and are the roots of x²-x+1=0, then the equation whose roots are ¹⁰⁰ and ¹⁰⁰ are

The amplitude of 5 +i (1- 5 )

If x= - ²-2, then the value of x⁴+3 x³+2 x²-11 x-6 is

If (a > 0, a R, z=a+2 i ) and (z|z|-a z+1=0 ) then

The roots of the equation (x^2-2 2 x+1=0 ) are

For the equation ( 1 x+a - 1 x+b = 1 x+c ), if the product of roots is zero, then the sum of roots is

The value of λ for which the loci arg z = π 6 and | z - 2 3 i | = λ on the argand plane touch each other is

If z 1 and z ¯ 1 represents adjacent vertices of a regular polygon of n sides and if I m z 1 R e z 1 = 2 - 1 , then n is equal to