Complex Number Calculator
Perform calculations with complex numbers in the form a + bi.
Result
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Polar Form
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Complex Numbers
A complex number is written as z = a + bi, where a is the real part and b is the imaginary part.
z = a + bi where i² = −1
Polar Form
z = r(cos θ + i·sin θ) = r·e^(iθ)
Where r = |z| = √(a² + b²) is the modulus, and θ = arctan(b/a) is the argument.
Operations
- Addition: (a+bi) + (c+di) = (a+c) + (b+d)i
- Multiplication: (a+bi)(c+di) = (ac−bd) + (ad+bc)i
- Modulus: |z| = √(a² + b²)