How do I find the trigonometric form of the complex

Tori Hines

Tori Hines

Answered question

2022-02-01

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

Answer & Explanation

vasselefa

vasselefa

Beginner2022-02-02Added 9 answers

An easy way to find any trigonometric for is by using complex numbers norms and the equation sin2(θ)+cos2(θ)=1.
Choosing a generic complex a+bi, we find its trigonometric form by dividing a for the numbers norm (a2+b2) which will result in the cosine of the θ angle that the number refers to.
a+bi=(a2+b2)cis(arccos(aa2+b2))
The trigonometric form of 3i is:
0+3i=(02+32)cis(arccos(002+32))=3cis(arccos(0))
Then, 3i in the trigonometric form is writen as 3cis(π2).

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