Download Complex Numbers Review

1.
2.
3.
4.
3x3  2 x 2  7 x  6  x  1
5 x3  3x 2  6  x  1
1.
2.
3.
3x3  5 x 2  4 x  2  3x  1
Compute (in terms of i)
4.
8
3x  5 x  2 
x 1
4
5x2  2 x  2 
x 1
2
3x 2  6 x  6
_i, -1, -i, 1
i, i 2 , i 3 , i 4
Warm-up
Answers
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
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Complex Number Review
Operations on Complex Numbers
Rationalizing Complex Numbers

Complex Numbers
Real Numbers
Imaginary Numbers
+
Real
a

I
Pure
Imaginary
bi
Standard Form:
a  bi

Add and subtract the real component and the
imaginary component separately.
(5  3i)  (2  4i) (10  2i)  (14  6i)
(3  i )
(4  4i )

Pg. P8 12-15
12.
(3  i)  (4  5i)
13.
(2  4.1i)  (1  6.3i)
14.
(2  3i )  (6  i)
15.
(2  4i)  (5  4i)

Multiply using FOIL (like quadratic factors)
(2  3i)(7  4i)
 14  21i  8i  12i 2
 14  29i  12(1)
 2  29i

Pg. P8 21-24
21.
(3  1)2
22.
(2  i )(4  3i )
23.
(3+5i)(3-5i)
24.
(5+3i)(2+6i)
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Complex Conjugates are complex numbers of
the form a + bi and a – bi.
Complex Conjugates can be used to
rationalize a complex denominator.
◦ Multiply numerator and denominator by the
complex conjugate of the denominator.
(5-3i) ● (1+2i)
(1-2i) (1+2i)
5+7i-6(-1)
2
5+10i-3i-6i
=
=
1-4(-1)
1-4i2
11+7i
=
5
=
11 + 7i
5 5
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Pg. P8: 12-15, 2124, 28-31
28.
5i
5i
29. 3  2i
4  i
30.
1  2i
2  3i
31.
3  4i
1  5i
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Review Complex Numbers
I can add, subtract, multiply and divide
complex numbers.
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Homework:
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◦ page P8: 12-15, 21-24, 28-31