*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:

*i*

^{2}=

*i*·

*i*= -1

*i*

^{3}=

*i*

^{2}·

*i*= -

*i*

*i*

^{4}=

*i*

^{3}·

*i*= 1

*i*

^{5}=

*i*

^{4}·

*i*=

*i*

*i*

^{6}=

*i*

^{4}·

*i*

^{2}= -1

*i*

^{7}=

*i*

^{4}·

*i*

^{3}=

*i*

^{3}= -

*i*

*i*

^{8}=

*i*

^{4}·

*i*

^{4}= 1

*i*

^{9}=

*i*

^{8}·

*i*=

*i*

*i*

^{10}=

*i*

^{8}·

*i*

^{2}= -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 + 6

*i*

I'll write another post on them later.

John, are you for real??? :)

ReplyDeleteI 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.

Congratulations,

Mrs Montenegro