Find the error in the following proof that z z Since z2 z

Find the error in the following proof that z = -z: Since z^2 = (- z)^2, it follows that 2Log(z) = 2Log(-z). This implies z^2 = e^Log(z) = e^Log(-z) = -z.

Solution

we have given z²=(-z)^{2 ,} it follows that 2Log(z)=2Log(-z)

Here the error is that Log of negative number i.e., Log(-z) is undefined.