Luttrell 2012
127
Name: ______________________
Date: _____
8n –Complex Numbers continued
Multipl
y
ing comple
x
numbers is similar to multipl
y
ing pol
y
nomials. There is just one e
x
tra step
of simplification and that is to remember
i
2
2
1
1
=
−
= −
(
)
.
For e
x
ample: (3 - 2
i
)(2 -
i
) = 6 - 3
i
- 4
i
+ 2
i
2
= 6 - 7
i
- 2 = 4 - 7
i
.
Multipl
y
and simplif
y
:
1. (2 + 3
i
)(3 - 2
i
)
2. (3 + 2
i
)(3 - 2
i
)
3. (1 - 2
i
)(1 - 2
i
) 4. (1-
i
)(2 + 2
i
)
Sometimes it is necessar
y
to know how far a point is from the origin, otherwise called modulus
or magnitude. The magnitude is indicated b
y
vertical bars around the comple
x
number. So | 4 +
3
i
| would be 5. How do
y
ou contrive that? By using the Pythagorean Theorem, use the origin
and given point as vertices of a right triangle.
Evaluate. Graph and show work with triangles.
5. | 3 - 2
i
|
6. |-2 - 2
i
|
7. |1 + 2
i
|
8. |-5 + 12
i
|
What can you do really fast to determine (without actually solving) if the equation has real roots?
If the discriminant (b
2
– 4ac) is negative there are no real solutions. Remember, negative
numbers under a square root are not possible with real numbers.
Comple
x
numbers are commonl
y
found when solving quadratic equations. Solve the following
for its x-intercepts, simplif
y
ing
y
our answers completel
y
.
9.
y
= 3
x
2
- 6
x
+ 4
10.
y
=
x
2
- 3
x
+ 3
11.
y
= 2
x
2
+ 7
x
+ 8
