Modulus-argument form

Which one of the following is a real number?

Circle your answer.

z⁴ z⁵ z⁶ z⁷

The complex numbers z and w are defined by

By evaluating the product zw, show that

Express 5 5i in the form reⁱ, where

The point on an Argand diagram that represents 5 5i is one of the vertices of an equilateral triangle whose centre is at the origin.

Find the complex numbers represented by the other two vertices of the triangle.

Give your answers in the form reⁱ, where

The complex number z is such that

where k is a real number.

Find the real part of z and the imaginary part of z, giving your answers in terms of k

Simplify

Tick () one box.

Find arg (4 7i) to the nearest degree.

Circle your answer.