Is there any method to calculate the value of (1+i)^n + (1-i)^n , without using the binomial theorem or Euler formulation?

Question

As (1-i) is the conjugate of (1+i) we can take the value of (1+i)+(1-i)= real part of (1+i)

But how to avoid Euler formula?

Answer 1

n is a positive integer.