Question

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

Answer 1

`z=3[cos(pi/2)+isin(pi/2)]=3isin(pi/2)`

When you have to convert a complex number, given in "rectangular form" ( `z=a+ib` ), to trigonometric form `z=r[cos(theta)+isin(theta)]` you need to evaluate:
1) the modulus `r` (using Pitagora's Theorem);
2) the argument `theta` (using trigonometry).

Graphically:

In your case you have: `z=0+3i=3i` so that:
1) `r=sqrt(3^2+0^2)=3`
2) `theta=arctan(3/0)=pi/2`

Graphically: