Complex Numbers - Definition

• The number i is given by:

1i

• We can also write the following:

2 1i • Numbers in the form of bi, where b is a real number,

are called Pure Imaginary Numbers.

• Another definition regarding imaginary numbers is as follows.

• Example 1:

12Simplify:

12 12i 4 3i 2 3i

a i a where a is a real number

• Example 2:

8 14 Determine the product:

8 14 8 14i i 2 8 14i

( 1) 2 2 2 2 7

4 7

• A complex number is given by…

a bi

• Example 3:

3 5i 2i 7

where a and b are real numbers.

All of the following are complex numbers:

• Example 4:

7 9

Put the complex number in standard a+bi form.

7 9 7 9i

7 3i

• When a radical is involved, the i usually precedes the radical, to make it clear the i is not under the radical.

5 2 3i

• Example 5:

would be written as …

5 2 3i