# Thread: Polar form of rectangular coordinates

1. ## Polar form of rectangular coordinates

How do write z=-5+2i in polar form?

2. ## Re: Polar form of rectangular coordinates

Originally Posted by derek1008
How do write z=-5+2i in polar form?
The principle value of the argument of a complex number $z=a+bi$ not on any axis is found by the following.
$Arg(z) = \left\{ {\begin{array}{rl} {\arctan \left( {\frac{b}{a}} \right),} & {a > 0} \\ {\arctan \left( {\frac{b}{a}} \right) + \pi ,} & {a < 0\;\& \,b > 0} \\ {\arctan \left( {\frac{b}{a}} \right) - \pi ,} & {a < 0\;\& \,b < \pi } \\ \end{array} } \right.$

So $Arg(-5+2i)=~?$ and $|-5+2i|=~?$