Question

How to express 1/(1+zcos(x)) in the form of a+bi? Where z= cos(x) +i sin(x).

Answer 1

`=frac{1+cos^2x}{1 + 3cos^2 x}-i frac{sin xcosx}{1 + 3cos^2 x}`

Explanation:

`frac{1}{1+(cosx + i sin x)cosx}`

`= frac{1}{1+cos^2x + i sin xcosx} * frac{1+cos^2x - i sin xcosx}{1+cos^2x - i sin xcosx}`

`=frac{1+cos^2x - i sin xcosx}{(1 + cos^2 x)^2 + sin^2 x cos^2 x}`

`=frac{1+cos^2x - i sin xcosx}{(1 + 2cos^2 x + cos^4x) + cos^2 x - cos^4 x}`