2017 HCI P2 Q2
The complex numbers $z$ and $w$ satisfy the following equations
$2z+3w=20$,
$w-z{{w}^{*}}=6+22\mathbf{i}$.
(i)
Find $z$ and $w$ in the form $a+b\mathbf{i}$, where $a$ and $b$ are real, $a\ne 0$.
[5]
(ii)
Show $z$ and $w$ on a single Argand diagram, indicating clearly their modulus. State the relationship between $z$ and $w$ with reference to the origin $O$.
[2]
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