math (please please please help)
posted by Lynn on .
How to convert into polar form?
z = 1  i
w = 1  √3i

The polar form expresses a complex number as:
z = z exp(i theta)
theta is the angle with the positive real axis.
For z = 1  i, we have:
z = sqrt(2)
Then it's easy to see that you can take theta = pi/4:
exp(i pi/4) = cos(pi/4)  i sin(pi/4) =
1/sqrt(2) (1i).
Then in case of
w = 1  √3i
you have:
w = sqrt(4) = 2
And you easly see that theta = pi/3
You can compute theta directly by taking arctan of imaginary part divided by the real part, but you may then need to add pi to this. If you multiply z by 1, theta changes by plus or minus pi, while the ratio stays the same. 
In polar form, the first is (1/sqrt(2),pi/4)
The second is (2,pi/3)