Math & Scientific
Complex Number Calculator
Complex Number: complex Number Calculator performs the operation on complex numbers a + bi, applying the rules for addition, multiplication and modulus/argument. Worked through below with real figures, and the calculator repeats the working on your own inputs — free, on-device, instant.
From your first number — real part, first number — imaginary part, operation and second number — real part, Complex Number Calculator computes the result via the standard method. No accounts, no uploads — just an instant way to work through a calculation.
About this calculator
Complex Number Calculator performs the operation on complex numbers a + bi, applying the rules for addition, multiplication and modulus/argument. It matters when you need the exact relationship checked quickly rather than worked through by hand. Worked below as (2 + 3i) + (1 − i) = (2+1) + (3−1)i = 3 + 2i ; multiplying (2+3i)(1−i) = 2 − 2i + 3i − 3i² = 5 + i. — and the calculator on this page repeats exactly that working for your inputs, instantly, and offline after load.
How to use
- Enter the real and imaginary parts of the first complex number.
- Choose the operation: add, subtract, multiply, or divide.
- Enter the real and imaginary parts of the second number, then press Calculate.
- Read the result in a + bi form, along with its modulus and argument.
Why use Complex Number Calculator
Fast
Calculations run in your browser. No round trip to a server.
Private
Your inputs never leave your device. Nothing is uploaded.
Free
No signup, no paywall, no ads-in-results, no watermarks.
Accurate
Based on standard, well-established formulas.
Mobile-ready
Optimised for phones, tablets, and desktops alike.
Transparent
Honest disclaimers wherever browser limits or regional rules apply.
Common uses
Use it for science-fair and project numbers
Use it for verifying answers from a textbook
Complex Number in statistics and data coursework
Use it for quick mental-math cross-checks
Use it when revising for exams
Complex Number in competitive-exam practice
Technical notes
Complex Number Calculator performs the operation on complex numbers a + bi, applying the rules for addition, multiplication and modulus/argument.
Inputs are taken exactly as entered, so check for typos before trusting an answer.
All arithmetic runs in your browser using double-precision floating point, so extreme inputs may show tiny rounding differences.
FAQ
How do I enter a complex number like 1 + 2i?
Type 1 in the real-part box and 2 in the imaginary-part box. You enter the two parts separately rather than typing the letter i.
What do modulus and argument mean in the result?
The modulus is the magnitude of the result (its distance from the origin), and the argument is its angle, shown in both radians and degrees.
What happens if I divide by zero?
If the second number is 0 + 0i, division is not defined and the calculator shows a clear message instead of a result.
Does the Complex Number Calculator send my data to a server?
No. The Complex Number Calculator runs entirely in your browser, so nothing you enter is uploaded, stored, or shared.
Worked example
(2 + 3i) + (1 − i) = (2+1) + (3−1)i = 3 + 2i; multiplying (2+3i)(1−i) = 2 − 2i + 3i − 3i² = 5 + i.