Find the quotient of the complex numbers.

Question

Find the quotient of the complex numbers:

 

2 * (sqrt 3) (cos (116 deg) + i sin (116 deg)) / 2(cos (82 deg) + isin (82 deg ))

Answer 1

Use DeMoivre's theorem; in division, the angle in the numerator will have the angle in the denominator subtracted, to give the resultant angle.  The answer therefore is √3(cos 34^o + i sin 34^o)