How do you divide $( 2i-1) / ( -i -1 )$ in trigonometric form?

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Answer 1 · 2018-07-02T11:53:26

$\sqrt{5/2}(\cos108.435^\circ-\sin 108.435^\circ)$

Given that

$\frac{2i-1}{-i-1}$

$=\frac{1-2i}{1+i}$

$=\frac{(1-2i)(1-i)}{(1+i)(1-i)}$

$=\frac{1-3i+2i^2}{1-i^2}$

$=\frac{1-3i+2(-1)}{1+1}$

$=\frac{-1-3i}{2}$

$=-1/2-3/2i$

Amplitude $=\sqrt{(-1/2)^2+(-3/2)^2}=\sqrt{5/2}$

Argument, $\theta=-(\pi-\tan^{-1}|\frac{-3/2}{-1/2}|)$

$\theta=-108.435^\circ$

$\therefore \frac{2i-1}{-i-1}$

$=\sqrt{5/2}(\cos(-108.435^\circ)+i\sin(-108.435^\circ))$

$=\sqrt{5/2}(\cos108.435^\circ-\sin 108.435^\circ)$

How do you divide ( 2i-1) / ( -i -1 )( 2i-1) / ( -i -1 ) in trigonometric form?