Multiplying Complex Numbers

Multiplying Complex Numbers

How to multiply complex numbers: examples and their solutions.

Example 1

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

Use the FOIL method
to multiply the complex numbers.

(+2i)⋅(+6i) = +12⋅(-1)
= -12

Powers of i

Add and subtract
the real numbers (green)
and the imaginary numbers (brown)
separately.

Example 2

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

Use the FOIL method
to multiply the complex numbers.

(+i)⋅(-5i) = -5⋅(-1)
= +5

Powers of i

Add and subtract
the real numbers (green)
and the imaginary numbers (brown)
separately.