Complex Number Calculator
Add, subtract, multiply and divide complex numbers in the form a + bi. Shows the result along with modulus |z| and argument arg(z).
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Result: 4 + 2i
|z| = 4.47214
arg(z) = 0.463648 rad (26.5651°)
How to Use the Complex Number Calculator
- Enter the first complex number in the form a+bi.
- Enter the second complex number.
- Pick an operation: add, subtract, multiply, or divide.
- Read the result, along with modulus |z| and argument arg(z).
使用场景
- •Electrical engineering — impedance, phasors, AC circuit analysis.
- •Signal processing and Fourier analysis.
- •Physics problems involving rotations and waves.
公式
(a+bi) ± (c+di) = (a±c) + (b±d)i. (a+bi)(c+di) = (ac−bd) + (ad+bc)i. Modulus |z| = √(a² + b²). Argument arg(z) = atan2(b, a).
常见问题
What notation does the input accept?
Forms like 3, 4i, -2i, 3+4i, -2-5i. Spaces are ignored. You can use i or j (engineering notation) for the imaginary unit.
What is the modulus of a complex number?
|z| = √(a² + b²). Geometrically, it is the distance from the origin to the point (a, b) in the complex plane.
What is the argument (arg) of a complex number?
arg(z) is the angle from the positive real axis to the vector (a, b), measured counter-clockwise. Calculated with atan2(b, a). Returned in both radians and degrees.
How is complex division done?
To divide (a+bi) by (c+di), multiply top and bottom by the conjugate (c−di): result is ((ac+bd) + (bc−ad)i) / (c² + d²).