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Complex Number to Polar Form Calculator — result sheet
Convert a complex number a + bi into magnitude, radians, degrees, and polar-form notation.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: r=√(a²+b²); θ=atan2(b,a); z=r(cosθ+i sinθ).
The polar form keeps the complex number’s magnitude and direction separate. atan2 preserves the quadrant that a one-argument arctangent would lose.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Real part a — minimum -1000000000; maximum 1000000000
- Imaginary part b — minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Real part a | 3 |
| Imaginary part b | 4 |
Magnitude =5; angle≈53.1301°; z=5∠53.1301°.
Assumptions and limits
- The input is a finite Cartesian complex number.
- The principal argument is returned in the interval (−π,π] when z is nonzero.
- A zero complex number has magnitude zero and a conventionally reported angle of zero.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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