convert z = A+Bi to z = r * e^(i*theta)?

Question

I need to convert Cartesian form to polar form. Use z = 2 - i*sqrt(3) for an example.

Answer 1

r=sqrt(4+3)=sqrt(7)
theta= arctan(sqrt(3)/2)=319.1degrees
so z=sqrt(7)exp(i*319.1)

Answer 2

For 'r', use the good ol' Pythagorean formula:

r = sqrt( A^2 + B^2)

For theta... since you have a right triangle (A,B,r), just use the trig. relationship:

theta = inverse-tangent (B/A)