Complex Number Calculator & Polar Form
Add, subtract, multiply, divide, raise to a real power or conjugate complex numbers. Convert rectangular and polar inputs and inspect the Euler form and Argand diagram.
About this complex number calculator & polar form
Add, subtract, multiply, divide, raise to a real power or conjugate complex numbers. Convert rectangular and polar inputs and inspect the Euler form and Argand diagram Computes exact algebraic and numerical metrics directly in your browser using IEEE 754 precision without round-trip latency.
Formula & calculation mechanics
The execution engine processes input tokens and applies transformations in the browser sandbox. Specifically, For multiplication, (a+bi)(c+di)=(ac−bd)+(ad+bc)i. Polar input uses r(cos θ+i sin θ), with r ≥ 0.
Worked numerical calculation
Scenario: Execute Complex Number Calculator & Polar Form with sample data to verify transformation accuracy and output formatting.
Sample input:
Illustrative output:
Domain range & precision boundaries
Binary64 arithmetic may round or underflow. Nonfinite intermediate values or results are rejected. Real noninteger powers use the principal argument in [−π, π]; zero to a nonpositive power is rejected. This is a numeric calculation, not symbolic algebra. Calculations run locally in the browser without a service or a paid dependency. No file output is required.
Calculations in Complex Number Calculator & Polar Form use standard IEEE 754 precision or exact rational models. Verify significant accounting or tax figures with authoritative references.
In-browser calculation boundary
Formula calculations and numeric evaluations in Complex Number Calculator & Polar Form run synchronously in the browser JavaScript engine with zero server telemetry.
Mathematical formulas & precision standards
Mathematical constants, IEEE 754 floating-point standards, and numerical analysis specifications:
- NIST Digital Library of Mathematical Functions, §1.2 — Elementary Algebra
- ECMAScript 2026, §6.1.6.1 Number Type
Complex Number Calculator & Polar Form verification · Audit standards
How to use it
- Choose the operation and input form for A and, when needed, B.
- Enter finite decimal numbers; choose degrees or radians for polar input.
- Calculate and compare the rectangular result, magnitude, argument, Euler form and vectors.
Frequently asked questions
How are complex numbers calculated?+
Operational requirements for "How are complex numbers calculated?" are verified in local memory during execution of Complex Number Calculator & Polar Form.
Which power and zero conventions apply?+
Argument is undefined at zero.
Where are values processed?+
Runtime handling of "Where are values processed?" executes synchronously in your browser tab without remote delays.
What should the -3 + 4i example output?+
For {"re":-3,"im":4}, the expected rectangular value is {-3,4}, magnitude 5, angleRadians 2.214297435588181 and angleDegrees 126.86989764584402.