Multiplying complex numbers

When multiplying complex numbers, many properties of real numbers such as the distributive property and/or FOIL, are also valid for complex numbers.

The multiplication of complex numbers is basically the same as the multiplication of polynomials.

Example #1:

Multiply 6 by 2i

6 × 2i = 12i

Example #2:

Multiply 4i by -3i

5i × -3i  = -15i²

             = -15(-1)  Substitute -1 for i²

             = 15

Example #3:

Multiply 5i by (-2i + 1)

5i × (-2i + 1) =  5i × -2i + 5i × 1  (Distributive property)

                    = -10i² + 5i

                    = -10(-1) + 5i

                    = 10 + 5i

Example #4:

Multiply (-2i + -3) by (-4i + 6)

(-2i + -3) × (-5i + 6)  = -2i × -5i + -2i × 6 + -3 × -5i + -3 × 6

                                = 10i² + -12i + 15i + -18 

                                = 10(-1) + 3i - 18

                                 = -10 + 3i - 18

                                 = -28 + 3i