If x, y, a and b are real numbers and if x+yi=a/(b+cosA+icosA) , show that (b^{2}-1)(x^{2}+y^{2}) +a^{2}= 2abx. (i= imaginary number)

I got a feeling that it may have something to do with the formula z+1/z = 2cosx and z-1/z =2isinx. But I just can't figure it out.