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.

After completing the multiplication, just replace any occurrences of i2 with -1 and then simplify by adding the real parts together and the imaginary parts together.

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

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