Complex Numbers

[anil86]

This is a thread for complex number problems in applied mathematics.

1. Prove that: 1 + cos x + cos 2x + .....cos (n - 1)x
= {1 - cos x + cos (n - 1)x - cos nx} / 2 (1 - cos x)

= 1/2 + [{sin (n - 1/2)x}/2sin (x/2)]


2. If a = cos x + i sin x, b = cos y + i sin y, c = cos z + i sin z, prove that

{(b + c) (c + a) (a + b)}/abc = 8 cos (x - y)/2 cos (y - z)/2 cos (z - x)/2

 

[stapel]

What have you tried? How far have you gotten? Where are you stuck?

Please be complete. Thank you!