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

1 Answer
Bernardo Russo G. Ferreira
Oct 2, 2014

An easy way to find any trigonometric for is by using complex numbers norms and the equation sin²(theta) + cos²(theta) = 1.

Choosing a generic complex a + bi, we find its trigonometric form by dividing a for the numbers norm (sqrt(a² + b²)) which will result in the cosine of the theta angle that the number refers to.

a + bi = (sqrt(a²+b²))*cis(arccos(a/sqrt(a²+b²)))
:.
The trigonometric form of 3i is:
0 + 3i = (sqrt(0² + 3²))*cis(arccos(0/sqrt(0²+3²))) =
= 3*cis(arccos(0))
Then, 3i in the trigonometric form is writen as 3*cis(pi/2).

Hope it helps.

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