Multiply Complex Numbers Calculator

Multiply two complex numbers in rectangular or polar form and read one consistent result in both representations.

|z₁| = 5|z₂| = 2.236068|z₁z₂| = 11.18034Angles: degrees

First number form

Switching form converts the current number.

First number real part (a₁)

Required finite decimal.

First number imaginary coefficient (b₁)

Enter the coefficient only, without i.

Second number form

The two inputs may use different forms.

Second number real part (a₂)

Required finite decimal.

Second number imaginary coefficient (b₂)

Negative values represent subtraction of an i term.

Angle unit

Applies to polar inputs and results.

Product in rectangular form

10 + 5i

Product in polar form

11.18034 ∠ 26.565051°

Real part

Imaginary coefficient

Magnitude

11.18034

Principal angle

26.565051°

Component calculation

Real: (3 × 2) – (4 × – 1) = 10. Imaginary: (3 × – 1) + (4 × 2) = 5.

Value	Real part	Imaginary coefficient	Magnitude	Principal angle
First number, z₁	3	4	5	53.130102°
Second number, z₂	2	– 1	2.236068	– 26.565051°
Product, z₁z₂	10	5	11.18034	26.565051°

Angles are normalized to the principal interval ( – 180°, 180°