i^2=i*i=(0,1)*(0,1)=(-1,0)=-1,
as we saw previously.
Sometimes imaginary numbers are first described in terms of being square roots of negative numbers.
The imaginary number i is a number such that if you have i i's of something than you have -1 of that thing.
Since that makes absolutely no sense to anyone seeing it for the first time, we'll just continue thinking about conplex numbers simply as point with the properties described here.
One final operation will be useful with complex numbers. If z=a+bi (z is just a point in the complex plane) we define
and call this the conjugate of z. Geometrically, this is just a reflection through the x-axis:
Let z,w be complex numbers. Simplify the following
1)
2)
3)
4)
5)
