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If a+ib = (root of 1+i) / (root of 1-i )then prove a^2 +b^2 =1

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    a+bi = √(1+i)/√(1-i)
    = √(1+i)/√(1-i) * √(1-i)/√(1-i)
    = √(1 - i^2) / (1-i)
    = √(1 - i^2) / (1-i) * (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

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