Higher Concepts of Mathematics
IMAGINARY AND COMPLEX NUMBERS
Example 2:
Multiply the following complex numbers:
(3 + 5i)(6 - 2i)=
Solution:
(3 + 5i)(6 - 2i)
= 18 + 30i - 6i - 10i2
= 18 + 24i - 10(-1)
= 28 + 24i
Example 3:
Divide
(6+8i) by 2.
Solution:
6
8i
2
6
2
8
2
i
3
4i
A difficulty occurs when dividing one complex number by another complex number. To get
around this difficulty, one must eliminate the imaginary portion of the complex number from the
denominator, when the division is written as a fraction. This is accomplished by multiplying the
numerator and denominator by the conjugate form of the denominator. The conjugate of a
complex number is that complex number written with the opposite sign for the imaginary part.
For example, the conjugate of 4+5i is 4-5i.
This method is best demonstrated by example.
Example:
(4 + 8i) ÷ (2 - 4i)
Solution:
4
8i
2
4i
2
4i
2
4i
8
32i
32i2
4
16i2
8
32i
32(
1)
4
16(
1)
24
32i
20
6
5
8
5
i
Rev. 0
Page 15
MA-05
