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Complex Number Calculator

Add, subtract, multiply, or divide two complex numbers A = a + b·i and B = c + d·i, or find the modulus, conjugate, and polar form of A — with the exact a + bi result, an Argand-plane graph, and step-by-step working.

Multiply:  (a + bi)(c + di) = (ac − bd) + (ad + bc)i
A = a (real) + b (imag) i B = c (real) + d (imag) i operation

Enter a, b for A and c, d for B. The B fields hide for single-number operations (modulus, conjugate, polar). Decimals and negatives are fine.

Results

Result
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Real part
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Imaginary part
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Modulus |·|
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Argument (degrees)
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Argand plane

A

Step-by-step (the algebra)