Square Roots, Complex Numbers

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. 

If you would like more information on complex numbers, write 
back and ask.

-Doctor Ethan, The Math Forum