Complex Number Calculator & Polar Form
Complex Number Calculator & Polar Form: Calculates modulus r = sqrt(3^2 + 4^2) = 5.0 and phase angle theta = atan2(4, 3) in radians and degrees.
About this complex number calculator & polar form
Complex Number Calculator & Polar Form — browser-based utility.
How this tool works
Calculation and parameter relationship: magnitude=√(re²+im²); angleRadians=atan2(im,re)
- Select “Raw JSON / Advanced” and paste the sample input.
- Click “Run locally”.
- Compare “Raw Output Data” with the example; revise inputs when an error is shown.
Worked example
Scenario: Use the following data to evaluate Complex Number Calculator & Polar Form
Sample input:
Processing: Calculation and parameter relationship: magnitude=√(re²+im²); angleRadians=atan2(im,re)
Illustrative output:
Limits and verification
Parameter domains and units: re,im ∈ ℝ; angleRadians ∈ [−π,π]; angleDegrees ∈ [−180,180]; magnitude ≥ 0. Results use binary64 floating-point numbers unless BigInt is stated. Result cards show up to 10 significant digits; raw output retains the serialized value. A null ratio means the model has no meaningful finite value for that ratio; it is not zero.
Examples demonstrate an expected workflow; they do not prove every input or every branch of an external specification. Check important results with an independent source before using them for money, security, compliance, safety, or irreversible file changes.
Browser processing boundary
Tool input is processed by code running in the browser and is not intentionally sent to a CZOA processing API. The page can still request ordinary site assets, analytics, or advertising when those services are enabled. Browser extensions and managed-device software remain outside this tool's control.
Relevant references
These references govern or help explain the format, protocol, or calculation used here. Listing a reference does not claim certification or complete implementation of every optional feature.
- NIST Digital Library of Mathematical Functions, §1.2 — Elementary Algebra
- ECMAScript 2026, §6.1.6.1 Number Type
Content owner: CZOA Tools · Last reviewed: 2026-09-15 · Review methodology
How to use it
- Select “Raw JSON / Advanced” and paste the sample input.
- Click “Run locally”.
- Compare “Raw Output Data” with the example; revise inputs when an error is shown.
Frequently asked questions
How are the polar values calculated from re and im?+
It returns the supplied rectangular coordinates, Math.hypot(re, im) for magnitude, Math.atan2(im, re) for radians, and radians × 180 / π for degrees.
Which JSON input is accepted by the complex calculator?+
Use JSON such as {"re":-3,"im":4}. Both fields are converted with Number; the tool does not parse algebraic text such as 3+4i.
What precision and angle boundaries apply?+
Magnitude is non-negative and atan2 returns an angle from -π to π. Arithmetic uses JavaScript binary64, so fractional values follow floating-point rounding.
What did the -3 + 4i browser vector verify?+
The fixture returned rectangular {-3,4}, magnitude 5, angleRadians 2.214297435588181 and angleDegrees 126.86989764584402; it ran locally.