How do I find the trigonometric form of the complex

Motalli21

Motalli21

Answered question

2022-01-30

How do I find the trigonometric form of the complex number 3i?

Answer & Explanation

coolbananas03ok

coolbananas03ok

Beginner2022-01-31Added 20 answers

Let z=3i
|z|=(3)2+(1)2=4=2
By factoring out 2,
z=2(3212i)=r(cosθ+isinθ)
by matching the real part and the imaginary part,
{r=2cosθ=32sinθ=12
θ=π6
Hence, z=2[cos(π6)+isin(π6)]
since cosine is even and sine is odd, we can also write
z=2[cos(π6)isin(π6)]

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