November 14,2010

Hey Guys Its Deep Here

Mr.P told us to collect the information about Imaginary Numbers.
                                      

Imaginary Numbers

Imaginary Numbers are numbers when squared gives a negative result.

Try

Let's try squaring some numbers to see if we can get a negative result:

2 × 2 = 4
(-2) × (-2) = 4 (because a negative times a negative gives a positive)
0 × 0 = 0
0.1 × 0.1 = 0.01

No luck! Always positive, or zero.

It seems like you cannot multiply a number by itself to get a negative answer ...

... but imagine that there is such a number (call it i for imaginary) that could do this: i × i = -1 Would it be useful, and what could we do with it?

Well, by taking the square root of both sides we get this:

Which means that i is the answer to the square root of -1.

And that is very useful ... by simply accepting that i exists we can solve things where we need the square root of a negative number.

Interesting Property

The Unit Imaginary Number, i, has an interesting property. It "cycles" through 4 different values each time you multiply:

i × i = -1, then -1 × i = -i, then -i × i = 1, then 1 × i = i (back to i again!) Have a Nice Day bye guys