Download Aim: How do we multiply or divide complex numbers? Do Now:

Aim: How do we multiply or divide
complex numbers?
Do Now:
1. Multiply: (3  2 x)( 2 
x)
2. Multiply:
(3  2 2 )( 2  2 )
3. Multiply:
(3  2i )( 2  i )
6 + 7x + 2x2
10  7 2
4 + 7i
HW: p.216 # 26,30,32,36,38,40,50,52
Multiplying
Treat the i’s like variables, then
change any i2 to -1
Ex:
 i (3  i )
2
 3i  i
 3i  ( 1)
 1 3i
Remember:
Ex: ( 2  3i )( 6  2i )
 12  4i  18i  6i
 12  22i  6(1)
 12  22i  6
 6  22i
The product of two complex numbers is a
complex number
2
Complex Conjugate
The conjugate of the complex number a + bi is the complex
number a – bi. For example, the conjugate of 5 + 2i is 5 – 2i.
Similarly, 3 – i and 3 + i are conjugates to each other.
The product of two complex numbers that are conjugates is
a real number
(5  2i)(5  2i)  25  10i  10i  4i
2
 25  4i
 25  4
 29
2
Divide 8 + i by 2 – i
8i
(8  i)  (2  i) 
2i
Write the division problem
in fractional form
15 10i


 3  2i
5
5
Simplify and write the result
in the form of a + bi
(8  i)( 2  i)
Multiply the conjugate of the

denominator, and the numerator
(2  i)( 2  i)
also multiply accordingly
2
16  10i  i
Multiply the binomials and

2
combine the like terms
4i
16  10i  1 15  10i


Simplify
4 1
5
Write the multiplicative inverse of 2 + 4i in the
form of a + bi
1
2  4i
1  (2  4i)

(2  4i)( 2  4i)
2  4i

4  8i  8i  16i 2
2  4i
2  4i


2
4  16
4  16i
2  4i
1 1


 i
20
10 5
The multiplicative inverse of 2 + 4i
Rationalize the denominator by
multiplying the conjugate of
the denominator on both the
numerator and denominator
Multiply
Simplify:
Simplify and write the result in
a + bi form
3  11i  1  2i
Multiply :

 1  2i  1  2i
(3  11i )( 1  2i )

(1  2i )( 1  2i )
 3  6i  11i  22i 2

1  2i  2i  4i 2
 3  5i  22(1)

1  4(1)
 3  5i  22

1 4
 25  5i

5
 25 5i


5
5
 5  i
Drill:
1. Multiply:
(7  i )(1  2i )
5 – 15i
2. Multiply: (3 – 2i)(3+2i)
13
3. Divide: (3  12i )
3i
4. Multiply:
 (4  i )
(3   49 )( 2   16 )
5. Write the multiplicative inverse of
9 – 2i and then simplify:
34 – 2i
9 2
 i
85 85