Math Playground
Numbers

Complex numbers

Real plus imaginary — a + bi. The numbers that close every equation.

A complex number has a real part and an imaginary part: a + bi.

Drag the complex number
realimaginary3 + 2i
3 + 2i
real part 3 · imaginary part 2
modulus |z| = √(3² + 2²) = 3.61
argument ≈ 33.69°
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(2 + 3i) + (1 + 4i)

Real with real, imag with imag: 3 + 7i.

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(1 + i)(2 − i)

FOIL: 2 − i + 2i − i² = 2 + i + 1 = 3 + i.