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Complex Numbers - Definition
• The number i is given by:
i  1
• We can also write the following:
i 2  1
• 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.
a  i a
where a is a real number
• Example 1:
Simplify:
12
12  i 12  i 4  3  2i 3
• Example 2:
8  14
Determine the product:
8  14  i 8  i 14
i
2
8 14
 (1) 2  2  2  2  7
 4 7
• A complex number is given by…
a  bi
where a and b are real numbers.
• Example 3:
All of the following are complex numbers:
3  5i
2i
7
• Example 4:
Put the complex number in standard a+bi form.
7  9
7  9  7  i 9
 7  3i
• When a radical is involved, the i usually precedes the
radical, to make it clear the i is not under the radical.
• Example 5:
5  2 3i
would be written as …
5  2i 3