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### Square root of a complex number.

```
Date: 6/6/96 at 12:32:47
From: Anonymous
Subject: The square root of a complex number.

My question is: Find the square root of 5+12i.  Hint: Let the square
root of 5+12i=a+bi.

This is how the question is in my math textbook.  I have been trying
it for a while now, but have been unable to get the answer.  I have
tried changing it to polar form and trying to get an answer from that,
but it does not seem to lead anywhere.

Thanks,
Lindsey
```

```
Date: 6/14/96 at 1:2:55
From: Doctor Beth
Subject: Re: The square root of a complex number.

If the square root of a+bi is 5+12i, then you know that
(a+bi)^2 = 5+12i.

This leads to the equation a^2 + 2abi - b^2 = 5+12i.  Whenever two
complex numbers are equal, their real parts and imaginary parts are
equal, so you have the 2 equations a^2 - b^2 = 5 and 2ab = 12.  Since
this is two equations with two unknowns, you can probably take it from
here.  (I did the problem and ended up with something that factored
very nicely.)

-Doctor Beth,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Exponents

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