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### Square Roots, Complex Numbers

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Date: Sat, 15 Jun 1996 00:03:07 -0400 (EDT)
From: Anonymous
Subject: Square Roots

x^2 = -9

I tried taking the square root of both sides. Is this impossible?
```

```
Date: Sat, 15 Jun 1996 09:25:18 -0400 (EDT)
From: Dr. Ethan
Subject: Re: Square Roots

Hello,

It depends on what you mean by impossible. If you want the answer
to be a real number like ones you are used to (like 2, 3.769,
17.55555.. , Pi, etc.) then it is impossible, but mathematicians have
come up with a whole area of mathematics and a whole system of
numbers that has no problem with x^2 = -9. They are called
complex numbers.

They use the symbol i to denote the square root of -1 so in your
problem, x = 3i.

-Doctor Ethan, The Math Forum
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Associated Topics:
High School Imaginary/Complex Numbers
High School Square & Cube Roots
Middle School Square Roots

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