If you use the identity z^n = cos(nθ)+isin(nθ) the equation becomes
Separating this into real and imaginary components gives the system:
Note that each of these is periodic with period 360/4 = 90 degrees (4 being the GCD of 8 and 28.)
This could be used along with a lot of identities to reduce and solve analytically, but I didn't feel like it. So I just made a table to get the solutions of each on the interval [0,90)
The cosines equation has 8 solutions and the sine has 12. The two in common are 15 and 75.
Add the period to give all the solutions sought:
Posted by Jer
on 2015-11-26 09:51:41