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ComplexLab
Complex arithmetic without the pain.
A complex number a + bi has a real part (a) and an imaginary part (b), where i is defined as √−1 — a number that doesn't exist on the ordinary number line but is essential for solving equations like x² = −1.
Electrical engineers use complex numbers to model AC circuits, and they're fundamental to signal processing and quantum mechanics — 'imaginary' doesn't mean 'not useful.'
What you entered
Add: combine real and imaginary parts separately
(3+1) + (4+2)i= 4 + 6iSubtract: same, but subtracting
(3−1) + (4−2)i= 2 + 2iMultiply: expand with i² = −1
(3×1 − 4×2) + (3×2 + 4×1)i= -5 + 10iModulus of z₁ (distance from origin)
√(3² + 4²)= 5Result
z₁ · z₂: -5 + 10i
Multiplying complex numbers uses i² = −1 to fold the imaginary terms back into a single real + imaginary result: -5 + 10i.