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

1 Answer

Feb 22, 2015

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!

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