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Complex Number Calculator

Add, subtract, multiply, divide, conjugate, convert to polar form, compute integer powers and n-th roots of complex numbers with RAD/DEG angle toggle and JSON export.

Inputs

Complex number A
+i
Complex number B
+i
Use parser fields for inputs like 3+2i, -4i, or 5.

Results

A
3 + 2i
B
1 − 4i
conj(A)
3 − 2i
conj(B)
1 + 4i
A + B
4 − 2i
A − B
2 + 6i
A × B
11 − 10i
A ÷ B
-0.294118 + 0.823529i
A in polar form
r = 3.605551, θ = 0.588003 rad
B in polar form
r = 4.123106, θ = -1.325818 rad
Aⁿ
5 + 12i (n = 2)
2-th roots of A
k=0: 1.817354 + 0.550251ik=1: -1.817354 − 0.550251i
Great for complex arithmetic practiceToggle RAD/DEG for argument output

How to use this tool

  1. Enter A and B via real/imag fields or parse strings like 3+2i directly.
  2. Switch RAD/DEG to control argument-angle display in polar output.
  3. Review arithmetic, conjugates, powers, and n-th roots, then copy or download JSON results.

Perfect online complex number calculator for courses

  • Experiment with sums, products, and quotients of a + bi numbers to build intuition.
  • See modulus and argument to connect algebraic complex arithmetic with the geometric view in the complex plane.
  • Use powers of A to explore rotations and scaling using r∠θ and cis(θ) forms.

What this complex number calculator supports

  • Addition, subtraction, multiplication, and division of complex numbers in a + bi form.
  • Conversion between rectangular form a + bi and polar / cis form (r, θ).
  • Integer powers and n-th roots of a complex number via De Moivre-style polar methods.

FAQ

Are angles in degrees or radians in this complex calculator?
You can toggle between radians and degrees in the input panel; all angle displays update immediately.
Can I compute square roots or roots of complex numbers?
Yes. Choose n in the n-th root selector and the calculator returns all roots for A.
What happens if B is 0 when dividing complex numbers?
Division by zero is undefined for complex numbers just like real numbers, so the calculator shows a clear warning for A ÷ B.

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