Multiplying Complex Numbers

Multiplying Complex Numbers

How to multiply complex numbers: examples and their solutions.

Example 1: Simplify (3 + 2i)(1 + 6i)

Simplify the given expression. (3 + 2i)(1 + 6i)

Use the FOIL method
to multiply these two complex numbers.

FOIL method

3⋅1 = 3
3⋅(+6i) = +18i
(+2i)⋅1 = +2i
(+2i)⋅(+6i) = +12⋅(-1)

Powers of i

18i + 2i = 20i

+12⋅(-1) = -12

3 - 12 = -9

So (given) = -9 + 20i.

Example 2: Simplify (4 + i)(8 - 5i)

Simplify the given expression. (4 + i)(8 - 5i)

Use the FOIL method
to multiply these two complex numbers.

4⋅8 = 32
4⋅(-5i) = -20i
(+i)⋅8 = +8i
(+i)⋅(-5i) = -5⋅(-1)

-20i + 8i = -12i

-5⋅(-1) = +5

32 + 5 = 37

So (given) = 37 - 12i.