MEDIUM
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The modulus of the complex number (1-i3)(cosθ+isinθ)(1+i)(cosθ-isinθ) is

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Important Questions on Complex Numbers and Quadratic Equations

MEDIUM
If z is a complex number satisfying z3+z-32, then the maximum possible value of z+z-1 is-
EASY
If z - αz + ααR is a purely imaginary number and z=2, then a value of α is :
MEDIUM
Let z=32+i25+32-i25. If Rz and Iz respectively denote the real and imaginary parts of z, then
MEDIUM

Let z1 and z2 be complex numbers satisfying z1=z2=2 and z1+z2=3. Then 1z1+1z2=

HARD
Let a be a fixed non-zero complex number with |a|<1 and w=z-a1-a-z, where z is a complex number. Then
EASY
Let z be a complex number such that the principal value of argument, argz>0. Then, argz-arg(-z) is
MEDIUM
If a and b are unit vectors and a+b=1, then a-b is equal to.
HARD
A complex number z is said to be unimodular if z=1. Let z1 and z2 are complex numbers such that z1-2z22-z1z2 is unimodular and z2 is not unimodular, then the point z1 lies on a 
MEDIUM
If 3+isinθ4-icosθ,θ0,2π, is a real number, then an argument of sinθ+icosθ is
MEDIUM
If a, b are the least and the greatest values respectively of z1+z2, where z1=12+5i and z2=9, then a2+b2=
EASY
Let z1 and z2 be complex numbers such that z1z2 and z1=z2. If Rez1>0 and Imz2<0, then z1+z2z1-z2 is
HARD
For any non-zero complex number z, the minimum value of |z|+|z-1| is
HARD
If z is a complex number of unit modulus and argument θ, then arg 1+z1+z- can be equal to given z-1
MEDIUM
If a>0 and z=(1+i)2a-i , has magnitude 25 , then z- is equal to:
EASY
A real value of x will satisfy the equation 3-4ix3+4ix=α-iβ (α,β are real), if