M314—Algebra II
Unit 7: The Quadratic Formula
Notes for 6.6: Add & Mult. Imaginary Numbers
Name: _______________________________
Date: ____________ Teacher: ___________
Section 6.6: Add and Multiply Imaginary Numbers
Part 1: Opener
Simplify the following numbers:
a) 5i3
b)-8i2
Part 2: Remember the powers of “i”
Powers of “i”
i1 = i
i2 = -1
i3 = -i
i4 = 1
Part 3 Multiplying Imaginary Numbers:
1. When multiplying imaginary numbers, treat the “i” like a _____________.
2. Simplify the number using powers of “___”.
3. You’re not finished until the “i”s are all simplified.
For Example:
 6i  5i
= ______________ = _______________ = ___________
(Multiply
5×6 and i×i)
Example 1:
 7i   8i
(i2 is -1)
(Multiply
30×-1)
Example 2:
 4i  2i ( 3i)(2)
Part 4 Multiplying Imaginary and Complex Numbers:
1. When multiplying with a complex number, treat it like a ____________.
2. When multiplying by two complex numbers, all you have to do is _______.
3. After to multiply, combine like terms if necessary.
4. Simplify using powers of “___”.
5. Write the answer as a complex number
For example:
3i(6  i)
= ____________ = _____________ = _____________
Distribute
the 3i to
both terms
Simplify
using powers
of “i”
Write the
answer as a
complex
number.
Here’s one you’ll have to FOIL:
(4  i)(2  4i) =
______________ = ____________________ = _____________ = _____________
FOIL
Simplify
Simplify
using powers
of “i”
Combine like
terms
Example 3:
Example 4:
i(5  6i)
Example 5:
6i(3  2i)
Example 6:
(7  2i)(1  i)
(2  2i)2
Part 5: Multiplying radicals with negative numbers under the radical.
Hint: Simplify the radical first!
For example:

5

25

= ______________ = ____________ = _____________ = _____________
Get rid of
the
negatives
under the
radicals
Example 7:

7
More Practice
1.  3i 
2.

3
7
  6i
2

3

Multiply
the
radicals
and the i’s
Simplify the
radical
Example 8:
Multiply as
necessary


6  3

3
