Complex Function Theory - The Algebra and Geometry of Complex Numbers

Question

I have problems with solving the following exercise.

4.11 Show that $\sqrt{zw} = \sqrt {z} \sqrt{w}$ need not be true for arbitrary complex numbers $z$ and $w$. Confirm that this formula is valid, however, if either $z$ or $w$ is a non-negative real number.

The exercise is found in the book "Bruce P. Palka - An Introduction to Complex Function Theory".

Somebody help me please.

Thanks.

Answer 1

Hint: You don't need to venture from the real numbers to get a counterexample. What happens if there is a minus sign under the square root?