sparknotes
Complex Numbers
Complex Conjugates and Dividing Complex Numbers
Complex Conjugates
Every complex number has a complex conjugate. The complex conjugate of a + bi is a - bi . For example, the conjugate of 3 + 15i is 3 - 15i , and the conjugate of 5 - 6i is 5 + 6i .
When two complex conjugates a + bi and a - bi are added, the result is 2a . When two complex conjugates are subtracted, the result if 2bi . When two complex conjugates are multiplied, the result, as seen in Complex Numbers, is a 2 + b 2 .
Dividing Complex Numbers
To find the quotient of two complex numbers, write the quotient as a fraction.
Then multiply the numerator and the denominator by the conjugate of the
denominator. Finally, simplify the expression:
|
= |
|
|
| = |
|
||
| = |
 . |
Examples:
(3 + 2i)÷(4 + 6i) =
?
| = |
|
||
| = |
|
||
| = |
|
||
| = |
|
||
| = |
|
||
| = |
 . |
(6 + 3i)÷(7 - 2i) = ?
| = |
|
||
| = |
|
||
| = |
|
||
| = |
|
||
| = |
 . |
(3 - i)÷(- 5 + i) = ?
| = |
|
||
| = |
|
||
| = |
|
||
| = |
|
||
| = |
|
||
| = |
 . |
Become a fan on Facebook
Follow us on Twitter
