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mihalych1998
2 months ago
11

Aye someone please help ?

Mathematics
1 answer:
AnnZ [12.3K]2 months ago
7 0

Answer:

To convert the specified complex polar form into the required rectangular format:

z1 = -3√2 - 3√2i

Detailed 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}}

By substituting the computed values into 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

Thus, the desired rectangular representation of the specified complex polar form is:

z1 = -3√2 - 3√2i

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I hope this is useful:)

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