Example 1: Complex Product

Compute the product of 3 + i6 and 7 - i.

(3 + i6) · (7 - i) = (3 · 7 - 6 · (-1)) + i(6 · 7 + 3 · (-1)) = 27 + i39.

The complex conjugate of z is formed by changing the sign of the imaginary part of z:

The product of a complex number with its conjugate is always a nonnegative real number, computed as follows.

(1)

(a + ib)(a - ib) = a² - iab + iab + b² = a² + b².

The quotient of two complex numbers can be computed by multiplying the numerator and denominator by the conjugate of the denominator, as follows.