Wednesday, March 16, 2011

Imaginary Numbers

Yesterday I learned about i. We use it to describe imaginary numbers.

This is the definition of i:

i =  -1 

Now if that is true, then the following is true:

i2 =i· i = -1

i3 = i2 · i = -i

i4 = i3 · i = 1

i5 = i4 · i = i

i6 = i4 · i2 = -1

i7 = i4 · i3 = i3 = -i

i8 = i4 · i4 = 1

i9 = i8 · i = i

i10 = i8 · i2 = -1

As you can see, every 4th power of i = 1.

So you can just divide i's exponent by 4 and the remainder will tell you the answer {1,i,-1,or -i}.

These are the questions I did yesterday.

A complex number has two parts - a real part and an imaginary part.

For example:

3 + 6i

I'll write another post on them later.

1 comment:

  1. John, are you for real??? :)
    I am an English teacher down in Brazil (you know where Brazil is, don´t you?) and I am trying to learn math really well because one day I want to be a math teacher, but, come on, you are already a math teacher!!! LOL.
    Keep up the good work. One day people from all over the world will look up to you and say: - Wow, I wish I were as smart as John is.
    Mrs Montenegro