Complex Numbers Questions

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| =...

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

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 ?...

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 of unit modulus and argument θ, then arg equals

If z ≠ 1 and is real, then the point represented by the complex number z lies :

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 complex numbers z = x + iy which satisfy the equation = l, lie on

If z = , then

The inequality |z - 4|

If z = x + iy and w = (1 - iz) / (z - i), then |w| = 1 implies that, in the complex plane

The points z1, z2, z3, z4 in the complex plane are the vertices of a parallelogram taken in order, if and only if

If a, b, c and u, v, w are the complex numbers representing the vertices of two triangles such that c = (1 - r) a + rb and w = (1 - r) u + rv, where r is a complex number, the the two triangles...

The value of is

If z1 and z2 are two non-zero complex numbers such that |z1 + z2| = |z1| + |z2|, then arg (z1) - arg (z2) is equal to...

The comples numbers sin x + i cos2x and cos x - i sin 2x are conjugate to each other, form...