If a and b are real numbers such that (2 + α)4 = a + bα, where α = -1 + i√32, then a + b is equal to:

If α and β are two complex numbers such that |α| = 1 and |β| = 1, then the value of the expression |β - α||1 - ᾱβ| is equal to:

The centre of the circle represented by |z + 1| = 2|z - 1| in the complex plane is:

Complex numbers z1 and z2 are (3 + 5i) and (5 + 7i) respectively. If the line segment joining z1 and z2 is rotated by 15° about z1 in the anticlockwise direction such that z2 becomes z3, then the value of z3 is:

If w is a non-real complex cube root of unity, then the equation |z - w|2 + |z - w2|2 = λ represents a circle if:

If α, β, and γ are the cube roots of -8, then what is α2p2 + β2q2 + γ2r2β2p2 + γ2q2 + α2r2 equal to?