Download Quick Crisp Review

Quick Crisp Review
• Complex Numbers
• Conjugates
• What happens when you multiply
conjugates?
You will be able to simplify expression
that contain complex numbers.
Cycle of "i"
i 1 i 1
1
5
i i i i
0
4
i  1 i  1
3
7
i  i i  i
2
6
To figure out where
we are in the cycle
divide the exponent
by 4 and look at the
remainder.
Graphing Complex
Numbers on the
Complex Plane:
Graph 3 + 4i
i
12
i
17
We use the
complex conjugate
to rationalize a
fraction that has a
complex number in
the denominator.
Multiply the numerator
and denominator by i
because the
denominator is not a
binomial expression
Example:
8i 1  3i

1  3i 1  3i
8i  24

1 9
8i  24

10
2i i

5i i
Example 2:
2i  i

2
5i
8i  24i 2

2
1  3i  3i  9i
2
2i  1

5
4i  12

5
You try it!
7
i
a)

 2i i
7i

 2i 2
b)
7i

2
5  i 1  2i

1  2i 1  2i
5  10i  i  2i 2

1  2i  2i  4i 2
5  9i  2
7  9i


5
1 4
Exit
How is dividing complex numbers similar to
rationalizing a denominator that has a
square root?
ACT
If x2 + 6x + 8 = 4 + 10x, then x equals which
of the following?
A) -2
B) -1
C) 0
D) 1
E) 2