Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

A quick one on complex numbers

Hi guys:)

Just a quick one - I wasn't sure how to find the square roots of (3 - 4i), does anybody have any ideas. I would have tried the binomial expansion, but I believe that it has a nice solution.

Thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A quick one on complex numbers

Hi Au101;

One way that is very quick is by inspection. By FOIL (2 + i) is not hard to get.

Or you can do it like this. Assume that it does have a square root.

This is solved by:

So in your case:

This leads to a quartic that is really a quadratic so it is easy to solve.
You will get 4 solutions and since the square root is positive you only accept c =2 and d=1.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: A quick one on complex numbers

Of course, thanks a lot, it was just a new style of question I saw whilst flicking through an exercise on complex numbers (which I did a few months ago) and I wanted to make sure that I hadn't forgotten everything!

Thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A quick one on complex numbers

Hi Au101;

complex numbers (which I did a few months ago) and I wanted to make sure that I hadn't forgotten everything!

What is a complex number? Where am I? And you are worrying about forgetting things?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.