Complex Number Polar Form Calculator
Complex Number Polar Form Calculator converts a rectangular complex number a plus bi into polar form, returning the modulus and the argument in degrees.
What this calculator does
The Complex Number Polar Form Calculator estimates your result instantly from the values you enter, using standard math & conversions formulas. Complex Number Polar Form Calculator converts a rectangular complex number a plus bi into polar form, returning the modulus and the argument in degrees. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Complex Number Polar Form Calculator
Give the real part a and imaginary part b of a complex number, and this calculator returns its polar form: the modulus r = √(a² + b²) and the argument θ = atan2(b, a) expressed in degrees.
The interpretation shows the result as r(cos θ + i sin θ).
Formula & Mathematical Calculation
Modulus r = f(Real part (a), Imaginary part (b))
Calculated according to standard math formulas implemented in the calculator core.
Calculation Example
For 3 + 4i, the modulus is √(3² + 4²) = √25 = 5, and the argument is atan2(4, 3) × 180 ÷ π = 53.130°. The tool shows Modulus r = 5 and Argument = 53.13 deg.
Key Benefits
- Converts rectangular a + bi to polar form instantly
- Reports both modulus and argument
- Uses atan2 so the argument lands in the correct quadrant
- Gives the argument in degrees for easy reading
How to Use this Calculator
-
Enter the real part
Type the real part a into the Real part field. -
Enter the imaginary part
Type the imaginary part b into the Imaginary part field. -
Calculate
Select Calculate and read the Modulus r and Argument in degrees.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Complex Number Polar Form Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.