How do you find the square root of 16(\cos(\frac{2\pi}{3})+i \sin

Kendall Holder

Kendall Holder

Answered question

2022-01-30

How do you find the square root of 16(cos(2π3)+isin(2π3))?

Answer & Explanation

ocretz56

ocretz56

Beginner2022-01-31Added 16 answers

Step 1
If r0and π<θπ then:
r(cosθ+isinθ)=r(cos(θ2)+isin(θ2))
So in our example:
16(cos(2π3)+isin(2π3))
=4(cos(π3)+isin(π3))
=4(12+32i)
=2+23i
Step 2
Note that this is the principal square root.
The other square root is:
4(cos(π3)+isin(π3))=223i

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