Square Roots of a Complex Number (1 Viewer)

[frog1944]

Hi,

In the syllabus it states that students should be able to "prove that there are always two square roots of a non-zero complex number".

How do you do this?

I haven't been able to find anywhere with a good proof and none of my textbooks have it.

Thanks

 

[braintic]

Here:

View attachment 2 square roots proof.pdf

 

[InteGrand]

Given any non-zero complex number r*cis(theta), it has two square roots (+/-)sqrt(r)*cis(theta/2). (These are clearly distinct if z =/= 0, i.e. r =/= 0.)

 

[frog1944]

Thank you very much for that braintic, I have not seen it proved that way. Thanks InteGrand