The complex numbers $z$ and $w$ satisfy $zw=5-12i$. Do not find $z$ and $w$ separately. Fi

Question

The complex numbers $z$ and $w$ satisfy $zw=5-12i$. Do not find $z$ and $w$ separately. Find $z^*w^*$.[1] Find $(zz^*)(ww^*)$, explaining how you regroup the factors.[2] Find $\operatorname{Re}(zw)$ and $\operatorname{Im}(zw)$ using sums and differences of $zw$ and $z^*w^*$.[2]

Accepted Answer

(a) $5+12i$ (b) $169$ (c) $\operatorname{Re}(zw)=5$, $\operatorname{Im}(zw)=-12$

Using a product and its conjugate

Using a product and its conjugate

Solution:

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