Hello Everyone, I was wondering, does anyone know of a proof that showed if a number is raised to the mth power, where m is a positive even number, the number is always real?
##(1+i)^2=1+2i-1=2i## Your claim will only be true for ##m=2## if the number is only real or imaginary. This is clear by expanding a complex number as a binomial. ##(a+bi)^2=a^2-b^2+2abi## In order for this to be real, either ##a## or ##b## must be zero. You should check the case when ##m=4## by squaring ##(a^2-b^2+abi)## to see what you get. Edit: I see that you figured it out as I was posting