Question

How do you find a trigonometric form of a complex number?

Answer 1

Let `z=x+iy` a complex number in algebraic form.

`z=r(cosphi+isinphi)` is its trigonometric form, where:

`r=sqrt(x^2+y^2)` is the modulus of the number and

• if `x>0`

`phi=arctan(y/x)` ,

• if `x<0`

`phi=arctan(y/x)+pi`,

• if `x=0` and `y>0`

`phi=pi/2`,

• if `x=0` and `y<0`

`phi=3/2pi`

• if `x=y=0`

It's all zero!