Unit 5  Objective 2  Basic Operations with Complex Numbers
Quick Review
We can add, subtract, multiply, or divide complex numbers.
Combine like terms when you add or subtract.
Example 1
Addition of complex numbers
If a+bj and c+dj are complex numbers then their sum is defined as:
(a+bj)+(c+dj)=(a+c)+(b+d)j
1. (9 + 2j) + (8 + 6j)  = (9 + 8) + (2 + 6)j 

 = 17 + 8j 

2. (6 + 3j) + (5  7j)  = (6 + 5) + (3  7)j 

 = 11  4j 
Subtraction of complex numbers
If a+bj and c+dj are complex numbers, then their difference is defined as:
(a + bj)  (c + dj) = (a  c) + (b  d)j
(distribute as before a+bjcdj)
Example 2
1. (3 + 4j)  (2 + j)  = (3  2) + (4  1)j 

 = 1 + 3j 

2. (8 + 4j)  (3 + 10j)  = (8  3) + (4  10)j 

 = 11  6j 
Multiplication of complex numbers
If a+bj and c+dj are any two complex numbers, then their product is defined as multiplying like binominals (FOIL) except replace j^2 with 1:
Example 3
1. (2 + 5j) (3  4j)  = (2) (3) + 2(4)j + 5j(3) + 5(4)j^{2} 

 = 6  8j + 15j  20(1)
= 6  8j + 15j + 20
= 26 + 7j 

2. (5 + 3j)^{2} = (5 + 3j) (5 + 3j)  = (5) (5) + 5(3j) + 3j(5) + (3j) (3j) 

 = 25 + 15j + 15j + 9j^{2}
= 25 + 15j + 15j + 9(1)
= 25 + 15j + 15j  9
= 16 + 30j 
Division of complex numbers
If a+bj and c+dj are complex numbers, then the quotient (a+bj)/(c+dj) is obtained by multiplying the numerator and denominator by the conjugate.
Example 4
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