Question 1408b

Complex Numbers

2008 Paper 2 Question 3 Variant

Question

The complex number

{w}

has modulus

{r}

and argument

{\theta,}

where

{0 < \theta < \frac{1}{2}\pi,}

and

{w^*}

denotes the conjugate of

{w.}

(a)

State the modulus and argument of

{p,}

where

p = \frac{w^*}{w}.

[2]

(b)

Given that

{p^2}

is real and negative, find the possible value(s) of

{\theta.}

[2]

Answer

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