Use De Moivre’s Theorem to find the indicated power of

Vikolers6

Vikolers6

Answered question

2021-12-11

Use De Moivre’s Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi and support with a calculator.
(13i)3

Answer & Explanation

Laura Worden

Laura Worden

Beginner2021-12-12Added 45 answers

a+bi=13i
Convert to polar form. (a,b)=(1,3) is in quadrant 4, so the angle must also agree.
r=a2+b2=12+(3)2=4=2
0=arctanba=arctan31=π3
13i=r(cos0+isin0)
=2(cos(π3)+isin(π3))
Use DeMoivres

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