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2-5-14 & 2-7-14(A); 2-6-14 & 2-10-14(B)
AM 2.1A To Simplify & Solve Complex Numbers
Things you don’t ever want to see…
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Active Learning Assignment?
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Lesson: To simplify complex numbers
Complex numbers are in the form a + bi, where a
is a real number and bi is the imaginary number.
EVERY NUMBER CAN BE EXPRESSED AS A
COMPLEX NUMBER.
How is “7” a complex number?
7 + ?i
7 + 0i
How is “2i” a complex number?
? + 2i
0 + 2i
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*
We know:  i   
Then:
*
i2 = –1
1 
2
If we square both sides
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Simplify in EXACT VALUE terms:
Ex.
25
1  25
1  25
Try :
7
i 7
Try :
32
i 16  2
4i 2
5i
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Simplify in EXACT VALUE terms:
Ex.
25  36
5i  6i
11i
Try :
81  64  1
9i  8i  1i
2i
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Ex.
2  12
Try :
18  4
i 2  i 12
i 18  i 4
i 2 2  12
i 2 18  4
1 2  12
1 18  4
1  24
1  72
1 4  6
1  36  2
2 6
Alternately:
1  18  2
2  9  2
2  3 2
6 2
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Ex.
24
18
i 24
i 18
24
18
24
18
4
3
4
3
3
2

3
3
2 3
3
{reduce}
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Try :
200
12
i 200
i 12
200
12
50
3
25  2
3
3
5 2

3
3
5 6
3
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Ex. (2 + 3i) + (5 – 4i)
{add real together and
imaginary together}
2 +5 + 3i – 4i
Ex. (5 – 2i) – (– 6 + 3i)
{add the inverse}
(5 – 2i) + (+6 + 3i)
11 – 5i
7–i
Try: (7 – 9i) + (11 – i)
18 – 10i
Try: (4 + 2i) – ( 7 – 2i)
– 3 + 4i
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Ex:
(3 + 5i) (4 – i)
Try: (6 –3i) (7 + i)
{FOIL or Distribute}
42 + 6i – 21i –3i2
3(4) + 3(-i) +5i(4) + 5i(-i)
45 – 15i
12 – 3i + 20i –5i2
(Since i2 = -1, Scratch & Change)
12 – 3i + 20i +5
17 + 17i
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Solve the complex equation:
Ex : x 2  100  0
x 2   100
x
2

100
x   10i
Try :
x2  4  0
x  4
2
x2 
4
x   2i
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Active Learning Assignment:
P. 28: 5,6, the Handout and Solve these:
1. x2 + 9 = 0
2. x2 + 25 = 0
3. x2 + 49 = 0
Journal Prompt:
1-8-13(A) or 1-9-13(B)
Describe something new that you discovered,
something you realized that you forgot, or some
connection that you made.
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