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Use DeMoivre's Theorem to find the following. Write your answer in
standard form.

Use DeMoivre's Theorem to find the following. Write your answer in standard form.-example-1
User Nonamelive
by
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1 Answer

5 votes

Answer:

Option C.

Explanation:

The given expression is


\left(√(2)cis (9\pi)/(20)\right)^5

It can be rewritten as


\left(√(2)\cos (9\pi)/(20)+i\sin(9\pi)/(20)\right)^5

According to De moivre's Theorem:


[r(\cos\theta+i\sin \theta)]^n=r^n(\cos n\theta +i\sin n\theta)

Using De moivre's Theorem, we get


(√(2))^5\left(\cos (9\pi* 5)/(20)+i\sin(9\pi* 5)/(20)\right)


=4√(2)\left(\cos (9\pi)/(4)+i\sin(9\pi)/(4)\right)


=4√(2)\left(\cos (2\pi +(\pi)/(4))+i\sin (2\pi+(\pi)/(4))\right)


=4√(2)\left(\cos (\pi)/(4)+i\sin (\pi)/(4)\right)


=4√(2)\left((1)/(√(2))+i(1)/(√(2))\right)


=4+4i

Therefore, the correct option is C.

User Somraj Chowdhury
by
7.8k points
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