Complex Numbers Questions

For a non-zero complex number z, let arg(z) denotes the principal argument with-π< arg(z) ≤π. Then, which of the following statement(s) is (are) FALSE ?...

If z is a complex number such that |z| ≥ 2, then the minimum value of

Let complex numbers α and lie on circles (x - x0)2 + (y - y0)2 = r2 and (x - x0)2 + (y - y0)2 = 4r2 respectively. If z0 = x0 + iy0 satisfies the equation 2|z0|2 = r2 + 2, then |α| =...

Let a, b, x and y be real numbers such that a - b = 1 and y #0. If the complex number z = x + iy satisfies Im(az+bz+1) = y, then which of the following is(are) possible value(s) of x ?...

Let z be a complex number such that the imaginary part of z is nonzero and a = z2 + z + 1 is real. Then acannot take the value

Let α, β be real and z be a complex number. If z2 + αz + β = 0 has two distinct roots on the line Rez = 1, then it is necessary that

The number of complex numbers z such that |z - 1| = |z + 1| = |z - i| equals

Let ω be a complex cube root of unity with ω ≠ 1. fair die is thrown three times. If r1, r2 and r3 are the numbers obtained on the die, then the probability that ωr1 + ωr2 + ...

The smallest positive integer n for which = 1, is

The conjugate of a complex number is . Then the complex number is

If z2 + z + 1 = 0, where z is a complex number, then the value of is

If the cube roots of unity are 1, ω, ω2 then the roots of the equation (x - 1)3 + 8 = 0, are

If z1 and z2 are two non-zero complex numbers such that |z1 + z2| = |z1| + |z2| then argz1 - argz2 is equal to...

If z and ω are two non-zero complex numbers such that |zω| = 1, and Arg (z) - Arg(ω) = , then is equal to...

If 1, ω, ω2 are the cube roots of unity, then ᐃ = is equal to

The locus of the centre of a circle which touches the circle |z - z1| = a and |z - z2| = b externally (z, z1 and z2 are complex numbers) will be...

For two unimodular complex numbers z1 and z2, if A = and B = , then A-1.B-1 is equal to -...

i57 + 1/i125 is equal to -

{1 + (− i)4n + 3} (1 − i) (n ∈ N) equals -

equals -