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) =?