How do you write the trigonometric form of \sqrt{3}+i?

Vanessa Hensley

Vanessa Hensley

Answered question

2022-02-01

How do you write the trigonometric form of 3+i?

Answer & Explanation

ebbonxah

ebbonxah

Beginner2022-02-02Added 15 answers

Answer: 3+i=2cos(π6)+2isin(π6)
Explanation:
A number a+ib can be written in trigonometric form as
rcosθ+irsinθ
As rcosθ=aand rsinθ=b, squaring and adding them we get r2=a2+b2.
As such for 3+i,r=(3)2+12=3+1=4=2
and cosθ=32and sinθ=12
i.e.θ=π6
Hence in trigonometric form 3+i=2cos(π6)+2isin(π6)

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