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Alex777 [14]
2 years ago
9

Use DeMoivre's Theorem to find (3cis*pi/6)^3

Mathematics
1 answer:
Sonbull [250]2 years ago
7 0

The correct value of (3cis(pi/6))³ is 27i.

<h3>What is Complex Number?</h3>

Complex numbers are numbers that consist of two parts — a real number and an imaginary number. Complex numbers are the building blocks of more intricate math, such as algebra.

Given the complex number in polar coordinate expressed as

z = r(cos∅+isin∅)

zⁿ =  {r(cos∅+isin∅)}ⁿ

According to DeMoivre’s Theorem;

zⁿ =  rⁿ(cosn∅+isinn∅)

Given the complex number;

(3cis(pi/6))³

= {3(cosπ/6 + isinπ/6)}³

Using  DeMoivre’s Theorem;

= 3³(cos3π/6 + isin3π/6)

=  3³(cosπ/2 + isinπ/2)

= 3³(0 + i(1))

= 27i

Thus, the correct value of (3cis(pi/6))³ is 27i.

Learn more about Complex number from:

brainly.com/question/10251853

#SPJ1

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