Question

Aye someone please help ?

Answer 1

Answer:

The required rectangular form of the given complex polar form :

z1 = -3√2 - 3√2i

Step-by-step explanation:

$z_1=6[\cos (\frac{5\pi}{4}) + i\sin(\frac{5\pi}{4})]...........(1)\\\\Now,\cos (\frac{5\pi}{4})=\cos(\pi+\frac{\pi}{4})\\\\=-\cos(\frac{\pi}{4})\\\\=-\frac{1}{\sqrt{2}}\\\\And,\sin (\frac{5\pi}{4})=\sin(\pi+\frac{\pi}{4})\\\\=-\sin(\frac{\pi}{4})\\\\=-\frac{1}{\sqrt{2}}$

On substituting the obtained values in equation (1)

$z_1=6[\frac{-1}{\sqrt{2}}-i\cdot \frac{1}{\sqrt{2}}]\\\\\implies z_1=-3\sqrt{2}- 3\sqrt{2}\cdot i$

Hence, the required rectangular form of the given complex polar form :

z1 = -3√2 - 3√2i