Question 1415

Complex Numbers

2015 Paper 1 Question 9 Variant

Question

The complex number

{w}

is such that

{w=a + b \mathrm{i},}

where

{a}

and

{b}

are non-zero real numbers. The complex conjugate of

{w}

is denoted by

{w^*.}

Given that

\frac{w^*}{w^2}

is purely imaginary, find the possible values of

{w}

in terms of

{a.}

[5]