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Home : Math & Science : Math Study Guides : Algebra II : Complex Numbers : Complex Conjugates and Dividing 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 a2 + b2.
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:
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Examples:
(3 + 2i)÷(4 + 6i) =?
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(6 + 3i)÷(7 - 2i) =?
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(3 - i)÷(- 5 + i) =?
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