Multiply Complex Numbers

How to multiply complex numbers: 2 examples and their solutions.

Example 1

Example

Solution

Use the FOIL method
to multiply these two complex numbers.

Multiply the first two terms.

3⋅1 = 3

Multiply the outer terms.

3⋅(+6i) = +18i

Multiply the inner terms.

+2i⋅1 = +2i

Multiply the last two terms.

+2i⋅(+6i)
= +12⋅i2
= +12⋅(-1)
= -12

Power of i

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

3 - 12 = -9
+18i + 2i = +20i

Add and Subtract Complex Numbers

So -9 + 20i is the answer.

Example 2

Example

Solution

Use the FOIL method
to multiply these two complex numbers.

Multiply the first two terms.

4⋅8 = 32

Multiply the outer terms.

4⋅(-5i) = -20i

Multiply the inner terms.

+i⋅8 = +8i

Multiply the last two terms.

+i⋅(-5i)
= -5⋅i2
= -5⋅(-1)
= +5

So
(4 + i)(8 - 5i)
= 32 - 20i + 8i + 5.

32 + 5 = 37
-20i + 8i = -12i

So 37 - 12i is the answer.