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

Recent Articles

  1. Probability Line - Definition and Examples

    Nov 21, 19 02:38 PM

    What is a probability line ? Things that you must know before doing problems ...

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

                                 Follow me on Pinterest

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.