Question 1410a

Complex Numbers

2010 Paper 1 Question 8 Variant

Question

The complex numbers

{z_1}

and

{z_2}

are given by

{1 - \sqrt{3} \mathrm{i}}

and

{- 1 + \sqrt{3} \mathrm{i}}

respectively.

(a)

Express each of

{z_1}

and

{z_2}

in polar form

{r(\cos \theta + \mathrm{i}\sin \theta), }

where

{r > 0}

and

{-\pi < \theta \leq \pi.}

Give

{r}

and

{\theta}

in exact form.

[2]

(b)

Find the complex conjugate of

\frac{z_1}{z_2}

in exact polar form

[3]

Answer

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