Question 1413b

Complex Numbers

2013 Paper 1 Question 8 Variant

Question

The complex number

{z}

is given by

{z=\mathrm{e}^{\mathrm{i}\theta},}

where

{r>0}

and

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

.

(a)

Given that

{w=(- 1 + \sqrt{3} \mathrm{i})z, }

find

{\left|w\right|}

in terms of

{r}

and

{\arg w}

in terms of

{\theta.}

[2]

(b)

Given that

{\displaystyle \arg \left( \frac{z^{6}}{w^2} \right) = -\pi,}

find

{\theta.}

[3]

Answer

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