Find the complex number $z$ in the form $x+y\,\mathbf{i}$ where $x$, $y\in \mathbb{R}$ such that $\f

Question

Find the complex number $z$ in the form $x+y\,\mathbf{i}$ where $x$, $y\in \mathbb{R}$ such that $\frac{\mathbf{i}z}{z-2{{z}^{*}}-2}=-1$. [3] Show that that for any complex number $z=r{{\mathrm{e}}^{\mathbf{i}	heta }}$, where $r>0$ and $-\pi $\frac{z}{z-r}=\frac{1}{2}-\frac{1}{2}\mathbf{i}\cot \left( \frac{	heta }{2} ight)$. [2]

Accepted Answer

(a) $z = -3 + \mathrm{i}$

2014 SAJC P2 Q4 [Modified]

2014 SAJC P2 Q4 [Modified]

Video Solution:

Solution:

Solution locked