- #1

kingwinner

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## Homework Statement

I'm beginning my studies in complex variables and have some questions...

Q1) We know that x

^{2}=9 => x=+/- √9 = +/- 3.

Suppose z^2 = w where z and w are COMPLEX numbers, then is it still true to say that

z = +/- √w ? Why or why not?

Q2) "Let az

^{2}+ bz + c =0, where a,b,c are COMPLEX numbers, a≠0.

Then the usual quadratic formula still holds."

My concern is with the √(b

^{2}-4ac) part. How can we find √(b

^{2}-4ac) when b

^{2}-4ac is a COMPLEX number?

For example, what does √(-1+4i) mean on its own and how can we find it? I know there is a general procedure(using polar form and angles) to solve for the nth root of a complex number (z^n=w), but I still don't understand what √(-1+4i) means on its own.

Even for real numbers, there is a difference between solving x

^{2}=9 and finding √9, right? So is there any difference between finding √(-1+4i) and solving z

^{2}=-1+4i for z using polar form and angles?

## Homework Equations

Complex variables

## The Attempt at a Solution

As shown above.

I hope someone can explain these. Any help is much appreciated!

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