Thread: Proof of polar coordinates

Let z e C.

0 is how I write theta below !!!

If z = r cos(0) + r sin(0) i in polar coordinates, then

z^-1 = r^-1 cos (-0) + r^-1 sin(-0) i and,

z^-1 = r^-1 cos (0) - r^-1 sin(0) i


How do I prove this? Thanks in advance!

Originally Posted by jzellt

Let z e C.

0 is how I write theta below !!!

If z = r cos(0) + r sin(0) i in polar coordinates, then

z^-1 = r^-1 cos (-0) + r^-1 sin(-0) i and,

z^-1 = r^-1 cos (0) - r^-1 sin(0) i


How do I prove this? Thanks in advance!

This is an application of DeMoivre's Theorem...

.


So .


These are some well-known identities:

and

(Check their graphs if you have to)...


So .