r exp(10/2). Here z = Let log(z) denote the branch of the logarithm with imaginary part...

 

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r exp(10/2). Here z = Let log(z) denote the branch of the logarithm with imaginary part lying in (-, ] and let z = exp(log(z)/2) = r exp(ie), r > 0, < 0 , and r refers to the positive square root of r. a) For which complex numbers z does z2 = z hold? b) Explain which step here is false, and why: 1 = : = (1)(1) = 11 = i = 1. r exp(10/2). Here z = Let log(z) denote the branch of the logarithm with imaginary part lying in (-, ] and let z = exp(log(z)/2) = r exp(ie), r > 0, < 0 , and r refers to the positive square root of r. a) For which complex numbers z does z2 = z hold? b) Explain which step here is false, and why: 1 = : = (1)(1) = 11 = i = 1.