Question

Find the numbers in the standard form $x+iy$
$\sqrt{2}\left(\cos \right(-\frac{\pi }{4})+i\sin (-\frac{\pi }{4}\left)\right)$

Answer 1

$\sqrt{2}(\cos \frac{-\pi }{4}+i\sin \frac{-\pi }{4})$

$\sqrt{2}(\cos \frac{\pi }{4}-i\sin \frac{\pi }{4})$ where $\cos (-\theta )=\cos \theta$ and $\sin (-\theta )=-\sin \theta$

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

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

$=1-i$ which is of the form $x+iy$

where $x=1$ and $y=-1$