complex numbers question

[hendo144]

given that (1+i)^n =x + iy, where x and y are real and n is an integer. prove that X^2 + y^2=2^n

cheers in advance

[sikhman]

take modulus of both sides (noting that |(1+i)^n| is the same as |1+i|^n) - pretty straightforward.

[addikaye03]

given that (1+i)^n =x + iy, where x and y are real and n is an integer. prove that X^2 + y^2=2^n

cheers in advance

yeah as sikhman (great name btw lol) take modulus of both sides:

|rt2|^n=rt(x^2+y^2)

x^2+y^2=(rt2)^2n

x^2+y^2=2^n