Simplify expressions with complex numbers
What is the imaginary
unit?
1 
GUIDED PRACTICE:
Simplify.
1. 25
2.
13
3.
20
4. 8 18
*********POWERS OF i
i0 =
i1 =
i2 =
i3 =
What patterns do you
see?
odd exponents
even exponents
Signs ______________
GUIDED PRACTICE:
Simplify.
1. 3i  8i
2
2.  3i 
5i 
How to simplify powers
larger than 3:
3. i 26
4. i 83
Divide the power by 4 and raise i to the
remainder!
page 2
Follow the order of
operations:
5.
First get rid of the negative under the radical,
then you can multiply
10  6
6. 2 12  3 3
a  bi
What is a complex
number?
The ____________ part is ALWAYS FIRST!!!
GUIDED PRACTICE:
Simplify.
7.  6  4i   1  3i 
8.  3  2i   5  4i 
9. 1  4i   3  2i 
10.  3  5i   3  5i 
What are conjugates?
(
)(
) Their product is a
_____________ number (no radical!).
page 3
How do you divide by a
complex number?
GUIDED PRACTICE:
Simplify.
11.
3i
2  4i
12.
5i
2i
13.
2i
2i
‘Electrical engineers use j
as the imaginary unit to
avoid confusion with the I
for current.”
GUIDED PRACTICE:
In an AC circuit, the
voltage E, current I, and
impedence Z are related
by formula E  I  Z . Find
the voltage in a circuit
with current 1  4 j amps
and impedence 3  6 j
ohms.
Rationalize with the ______________ of
the denominator.