We aren't able to find a square root of -1 using the numbers we already know about, so we had to invent one! We call it i, which stands for "imaginary", though actually i is a perfectly good number. A number of the form a+bi is called a complex number.

1) Add the following pairs of numbers:

5i + 3i =

(2+2i) + i =

(5+3i) + (8+12i) =

2) Draw the complex plane and plot the following numbers: i, -3i, 4-i, -1, -2-2i











3) Multiply the following pairs of numbers:

i * i =

3i * 4i =

-2i * 5i =

4) Do you think that (4+3i) * (5+7i) = 20 + 21i? Why or why not?




5) Try to find a square root of i. Note: this one is tricky!