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Complex Number Calculator

Add, subtract, multiply and divide complex numbers, with modulus, argument, conjugate and polar form.

Related tools

All Algebra & equations tools →
Eigenvalue and Eigenvector Calculator (2×2 and 3×3, complex supported)Characteristic polynomial, exact eigenvalues — rational, surd like (1±√5)/2, or complex like ±i for a rotation — with eigenvectors, algebraic and geometric multiplicities, and a clear verdict on diagonalizability.Amicable Number CheckerCheck whether two numbers are amicable — or give just one and get its candidate partner plus the verified loop, with perfect and sociable numbers identified.e Digits Calculator (Euler's Number)Compute up to 1,000 decimals of Euler's number e from the series Σ 1/k!, with digit frequencies, a digit search and the 1828 1828 trap explained.Fibonacci Number CheckerTest any number up to 60 digits with the exact 5n^2 +/- 4 identity, with its index, its neighbours in the sequence and the ratio compared with the golden ratio.Five Number Summary CalculatorGet the minimum, quartiles and maximum of a dataset with the IQR, the outlier fences and a box plot, in three quartile conventions.Number of Digits CalculatorCount the digits of any integer in any base from 2 to 36, with the digit sum, product, first and last digit, and palindrome and repdigit flags.Number Pattern FinderFind the rule behind a sequence: arithmetic, geometric, quadratic, cubic, Fibonacci, powers, triangular, factorial, primes or a linear recurrence, with the difference table and the next terms.Perfect Number CheckerTest whether a number is perfect, abundant or deficient from the sum of its proper divisors, with the Euclid-Euler theorem explained.

Complex Number Calculator works straight from this page — free, instant, nothing to install. It sits under Algebra & equations in our catalogue, alongside Eigenvalue and Eigenvector Calculator (2×2 and 3×3, complex supported) and Amicable Number Checker.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Complex Number Calculator do?

Add, subtract, multiply and divide complex numbers, with modulus, argument, conjugate and polar form.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

How is Complex Number Calculator different from Eigenvalue and Eigenvector Calculator (2×2 and 3×3, complex supported)?

They sit next to each other but answer different questions: Eigenvalue and Eigenvector Calculator (2×2 and 3×3, complex supported) is the one to open when you need it to characteristic polynomial, exact eigenvalues — rational, surd like (1±√5)/2, or complex like ±i for a rotation — with eigenvectors, algebraic and geometric multiplicities, and a clear verdict on diagonalizability. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Amicable Number Checker is the closest one after this: Check whether two numbers are amicable — or give just one and get its candidate partner plus the verified loop, with perfect and sociable numbers identified.

What else is worth having open alongside it?

e Digits Calculator (Euler's Number) and Fibonacci Number Checker — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The algebra is symbolic where the expression allows it and numeric otherwise, and the tool says which it used. Exact results are given as fractions or radicals rather than rounded decimals.

Further reading

All guides →
How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.