Complex numbers

Multiple choice questions

Q1

Given z² = 4(cos 3π/2 + i sin3π/2). which of the following is equal to z?

Q2

Suppose that z1 and z2 are two complex numbers such that z1z2 = 1.

Given that z,1 = re^θ, which of the following is equal to z2?

Q3

Suppose a nonzero complex number z1 is multiplied by 1+i / 1-i to produce the complex number z2

Which of the following best describes z2 in relation to z1 ?

Q4

Given that z^π =(-1)^3i, which of the following is equal to z?

Q5

The Argand diagram below shows the complex number z.

Which of the following best represents z²?