maths
posted by haritha on .
If a+ib = (root of 1+i) / (root of 1i )then prove a^2 +b^2 =1

a+bi = √(1+i)/√(1i)
= √(1+i)/√(1i) * √(1i)/√(1i)
= √(1  i^2) / (1i)
= √(1  i^2) / (1i) * (1+i)/(1+i)
= √2(1+i)/2
= √2/2 + √2/2 i
so a = √2/2 and b=√2/2
and a^2 + b^2 = 2/4 + 2/4 = 1