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### The Imaginary Number J

```
Date: 09/14/2001 at 12:43:13
From: Sam Tomlinson
Subject: (J) Imaginary numbers

One of my maths teachers says that you cannot find the square root of
a minus number, especially minus one. I say that the square root of
minus one equals J and is an imaginary number. My other maths teacher
agrees with me and I would just like to check with somebody else.
```

```
Date: 09/14/2001 at 13:45:41
From: Doctor Peterson
Subject: Re: (J) Imaginary numbers

Hi, Sam.

They're both right. At your level, if you haven't officially learned
about imaginary numbers, or in general when you are working only with
real numbers, you can't take the square root of a negative number. But
when you have learned about imaginary and complex numbers, and are
working in a setting where complex numbers are allowed, then you can.

It's just like what happens with negative numbers. Young children
learn that they can't subtract a larger number from a smaller number.
That's still true, even after you've learned about negative numbers,
when you are working on a problem for which negative numbers don't
make sense, such as calculating how many cookies are in the cookie
jar, or subtracting digits in a large subtraction problem. But once
you know about negative numbers, you can solve problems you couldn't
solve before - IF you check that negative numbers make sense in the
problem you are solving.

See the Dr. Math FAQ on imaginary numbers:

http://mathforum.org/dr.math/faq/faq.imag.num.html

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Imaginary/Complex Numbers

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