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: *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.

Mrs MontenegroDecember 27, 2011 at 6:40 pmJohn, 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.

Congratulations,

Mrs Montenegro