# 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) = ?

 = = = = = = .

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