Download CLASSROOM COPY – DO NOT WRITE ON!!! CRS NCP 605

CW#47: Multiply Complex Binomials
Geometry
CLASSROOM COPY – DO NOT WRITE ON!!!
NCP 605 – Multiply two complex numbers
CRS
Objectives
5.11 Multiply two complex numbers
5.12 Multiply two binomials that include complex numbers
**Teacher Notes: The students only have a classroom copy. All writing should be done in their graph paper notebooks.
All writing in italics is not on the classroom copy. The italics represent the notes you should write on graph paper for kids
to copy down**
Reflect
In your notebooks, reflect on the following:

What is an imaginary number?

Why does i² equal -1?

Describe how you would simplify i 42 ?
Mixed Review
1) Simplify:
4) Simplify:
7) Simplify:
3
2) Solve:
3)
 216 x 3 y 7
5) Simplify: Simplify completely:
50
 25 x 2
8)Simplify: 3  343
9) Simplify: 6i(3i² – 2)
11) Simplify: 2i  3i  15  2i 2
12) What are the roots of the
equation k 2  4k  3 ?
10) Simplify
6  9  2  144
6) Simplify: Simplify:
PUSH IT TO THE LIMIT.
Multiply Complex Binomials

FOIL or BOX!!

Remember that i² = -1!!
Example 1: (3 + 2i)(4 – 5i)
Example 2: (3 – 2i)²
1) (-4 + 7i)(10 - 4i)
2) (4 -2i) (3+ 5i)
3) (-2 - 6i)(-8 - 4i )
4) -8i – 4(i + 3i²)*Note: Order of
operation! Multiply before subtracting!
6) Multiply and simplify: (-3 + 4i)2.
5)
A.
B.
C.
D.
-9 + 16i
-7 – 24i
9 – 16i
6 + 9i
The voltage E, current I, and impedance Z in a circuit are related by E  I  Z . Find the voltage (in volts) in
each of the following circuits given the current and impedance.
7) I  1  3 j amps, Z  7  5 j ohms
8) I  2  7 j amps, Z  4  3 j ohms
9) Which of the following is equivalent to i33?
10) CHALLENGE. Simply:
A.
B.
C.
D.
(1  3i)( 2  2i)(1  2i)
1
i
-1
-i
11) CHALLENGE. Simplify:
12) CHALLENGE. Multiply and simplify: (2 – 3i)4
(2  i)(3  2i)(1  4i)
A.
B.
C.
D.
8 – 12i
16 – 81i
-58 + 112i
-119 + 120i
PUSH IT TO THE LIMIT.
CW#47: Multiply Complex Binomials
Geometry
CLASSROOM COPY – DO NOT WRITE ON!!!
NCP 605 – Multiply two complex numbers
CRS
Objectives
5.11 Multiply two complex numbers
5.12 Multiply two binomials that include complex numbers
**Teacher Notes: The students only have a classroom copy. All writing should be done in their graph paper notebooks.
All writing in italics is not on the classroom copy. The italics represent the notes you should write on graph paper for kids
to copy down**
Reflect
In your notebooks, reflect on the following:

What is an imaginary number?

Why does i² equal -1?

Describe how you would simplify i 42 ?
Mixed Review
1) Simplify:
4) Simplify:
7) Simplify:
3
2) Solve:
3)
 216 x 3 y 7
5) Simplify: Simplify completely:
50
 25 x 2
8)Simplify: 3  343
9) Simplify: 6i(3i² – 2)
11) Simplify: 2i  3i  15  2i 2
12) What are the roots of the
equation k 2  4k  3 ?
10) Simplify
6  9  2  144
6) Simplify: Simplify:
PUSH IT TO THE LIMIT.
Multiply Complex Binomials
Example 1: (3 + 2i)(4 – 5i)
Example 2: (3 – 2i)²
1) (-4 + 7i)(10 - 4i)
2) (4 -2i) (3+ 5i)
3) (-2 - 6i)(-8 - 4i )
4) -8i – 4(i + 3i²)*Note: Order of
operation! Multiply before subtracting!
6) Multiply and simplify: (-3 + 4i)2.
5)
A.
B.
C.
D.
-9 + 16i
-7 – 24i
9 – 16i
6 + 9i
The voltage E, current I, and impedance Z in a circuit are related by E  I  Z . Find the voltage (in volts) in
each of the following circuits given the current and impedance.
7) I  1  3 j amps, Z  7  5 j ohms
8) I  2  7 j amps, Z  4  3 j ohms
9) Which of the following is equivalent to i33?
10) CHALLENGE. Simply:
A.
B.
C.
D.
(1  3i)( 2  2i)(1  2i)
1
i
-1
-i
11) CHALLENGE. Simplify:
12) CHALLENGE. Multiply and simplify: (2 – 3i)4
(2  i)(3  2i)(1  4i)
A.
B.
C.
D.
8 – 12i
16 – 81i
-58 + 112i
-119 + 120i
PUSH IT TO THE LIMIT.