Name Date
WORKSHEET 7.10: SIMPLIFYING COMPLEX NUMBERS
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A complex number is a number of the formx+yi, wherexandyare real numbers.xis the
‘‘real’’ part ofx+yi.yis the ‘‘imaginary’’ part. Use the guidelines below to simplify complex
numbers:
- Addition or subtraction:Combine the real parts, then combine the imaginary parts.
- Multiplication:Use FOIL. Simplify by combining the real parts, then combine the imagi-
nary parts. Replacei^2 by−1. - Division:Multiply the numerator and denominator by the conjugate of the denominator.
Simplify the numerator. Simplify the denominator. Replacei^2 by−1.
EXAMPLES
Addition:(3+ 2 i)+(6− 7 i)= 9 − 5 i
Subtraction:(3+ 2 i)−(6− 7 i)= 3 + 2 i− 6 + 7 i=− 3 + 9 i
Multiplication:(3+ 2 i)(6− 7 i)= 18 − 9 i− 14 i^2 = 18 − 9 i−14(−1)= 32 − 9 i
Division:
3 + 2 i
6 − 7 i
=
3 + 2 i
6 − 7 i
·
6 + 7 i
6 + 7 i
=
18 + 33 i+ 14 i^2
36 − 49 i^2
=
18 + 33 i+14(−1)
36 −49(−1)
=
4 + 33 i
85
DIRECTIONS: Simplify each expression.
(3− 6 i)+(4+ 8 i) 2. (1− 2 i)−(3+i)
(1−i)(4−i) 4. (2+ 3 i)(1+ 2 i)
5. (2− 3 i)(2− 3 i) 6. (4− 2 i)(1−i)
(1+ 3 i)
(2+i)
8.
(3− 4 i)
(2− 3 i)
CHALLENGE:Andrew said that (3−i)+(2−i)= 6 − 5 i+i^2 or 5− 5 i.Ishe
correct? If he is incorrect, explain what he might have done wrong and
provide the correct answer.
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Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.