Algebra & Equations

Complex Multiplication

Multiply two complex numbers.

Formula

Formula
(ac−bd) + (ad+bc)i

Variables

SymbolDefinitionType & rangeUnitsRole
a, b first number real number (ℝ) real input
c, d second number real number (ℝ) real input

Try it yourself

Interactive calculator
Result

Worked examples

Example 1
Givena (real) = 3, b (imag) = 2, c (real) = 1, d (imag) = -4
Result11 + -10i
Example 2
Givena (real) = 1, b (imag) = 1, c (real) = 1, d (imag) = -1
Result2 + 0i