is there any easy way to calculate (x+iy)^n +(x-iy)^n

Question

I know the usual binomial theorem method but i wanted to know some easier method

Answer 1

Another way is to convert the two complex numbers to trigonometric form z = r (cosθ+isinθ) and then when raised to the nth power you'll have zⁿ = rⁿ(cos nθ+isin nθ).  This may be helpful!