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.