Complex Analysis Square Root of Z^2

It is plainly true of any complex number z that either $\displaystyle \sqrt{z^2}=z$ or $\displaystyle \sqrt{z^2}=-z$. Identify the set of z for which the minus set represents the proper choice. I believe the answer is the set of imaginary numbers, but am not sure. ?

Re: Complex Analysis Square Root of Z^2

I don't understand what you mean by "the proper choice". Why would either of those be "proper" or "not proper"? "Proper" in what sense?

Re: Complex Analysis Square Root of Z^2

I took the question to mean for which set is -z the right answer? Normally, in the real numbers, we use z as the answer. So I am thinking for for -z to be the "correct" answer, we would be in the imaginary numbers. Right?

Re: Complex Analysis Square Root of Z^2

Quote:

Originally Posted by

**tarheelborn** It is plainly true of any complex number z that either $\displaystyle \sqrt{z^2}=z$ or $\displaystyle \sqrt{z^2}=-z$. Identify the set of z for which the minus set represents the proper choice. I believe the answer is the set of imaginary numbers, but am not sure. ?

Assuming that this is the language of your textbook and/or your instructor, What is meant by "**proper choice**"? What specifically is this referring to?

I suspect that your answer for the question in the Original Post is incorrect, but it's not possible to be sure about this without a precise definition of "**proper choice**".