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Free online complex number calculator. Add, subtract, multiply, and divide two complex numbers instantly. Perfect for circuit analysis and signal processing.
Enter the real and imaginary parts for each complex number. Leave blank for 0. For example, for 3 + 4i, enter 3 in the real part and 4 in the imaginary part.
Enter two complex numbers and select an operator to see the result.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
Enter each number by its real part and imaginary part: 3 + 4i is represented by real part 3 and imaginary part 4. The calculator combines two inputs using addition, subtraction, multiplication, or division. Blank part fields are treated as zero, so a purely real number can be entered without an imaginary component.
For an output z = x + yi, the modulus is its distance from the origin, |z| = √(x² + y²). The argument is its direction from the positive real axis; this calculator reports the principal angle in both radians and degrees. It also shows the conjugate x − yi, worked arithmetic steps, and a point on the complex plane.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Enter its real and imaginary coefficients separately. For 3 + 4i, enter 3 and 4.
For 2 − i, enter 2 as the real part and −1 as the imaginary part. Do not type the letter i into a coefficient box.
Choose add, subtract, multiply, or divide. The result refreshes from the two inputs.
Check the rectangular result, modulus, argument, conjugate, displayed steps, and plotted point. Copy or reset the values when needed.
Example: (3 + 4i) + (2 − i) = 5 + 3i. The modulus is √34 ≈ 5.831, and the principal argument is about 0.540 radians or 30.96°.
Use cases
See how the tool fits into real work and everyday tasks.
Compare a hand-worked sum, product, or quotient with the displayed result and intermediate steps.
Use the plotted point and modulus/angle fields to connect rectangular coordinates with magnitude and direction.
Check a single pairwise arithmetic operation before carrying the result into a larger worksheet or analysis.
Q&A
Find concise answers to common questions and confusing cases.
No. Enter the real and imaginary coefficients in separate fields. For negative imaginary values, include the minus sign in that coefficient.
The principal angle is measured from the positive real axis. A point below that axis has a negative principal angle; degrees and radians are two units for the same angle.
Division is rejected when both components of the divisor are zero. Enter a nonzero real or imaginary component to continue.
No. It performs one of four arithmetic operations on two complex numbers. It does not solve equations, process matrices, or evaluate symbolic expressions.
Notes
Review scope, result limitations, and important precautions before use.
This is numerical arithmetic on two inputs, not a symbolic algebra system. A zero result has no defined direction, so its argument should not be interpreted as a meaningful angle. Floating-point results are displayed as decimal approximations; retain exact forms separately when a proof or exact answer is required.
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