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Updated 2026-03-01 UTC
Polar to Rectangular — Complex Number Conversion
Convert complex numbers from polar to rectangular form with GetCalcMaster. Includes phasor tips and verification checks.
This guide explains polar→rectangular conversion for complex numbers, with practical tips for signals and phasor-style problems.
Important: Educational use only. Confirm angle units (degrees/radians) and rounding rules when converting.
What this calculator is
The Complex Number Calculator is an interactive tool inside GetCalcMaster. It’s designed to help you explore scenarios, understand formulas, and document assumptions.
Key features
- Rectangular form: a + j b
- Polar form: r∠θ
- Use cos/sin: a=r cosθ, b=r sinθ
Formula
Given r∠θ: a = r·cos(θ), b = r·sin(θ)
Result: a + biQuick examples
10∠30° → 8.660 + 5.000i5∠53.13° → 3 + 4i2∠(−90°) → 0 − 2i
Verification tips
- Confirm θ units (degrees vs radians) before converting.
- Sanity check: r should equal √(a² + b²).
- Angles can be normalized (e.g., −90° = 270°).
Common mistakes
- Swapping sin and cos (a uses cos, b uses sin).
- Forgetting the sign of the imaginary part for negative angles.
- Using atan instead of atan2 when reversing the conversion.
How to use it (quick steps)
- Enter complex numbers in the supported form (a+bi, polar, etc.).
- Choose the operation (add/multiply, magnitude/phase, conversions).
- Review both rectangular and polar interpretations where relevant.
- Copy/export results or send them to Notebook for future reference.
Related tools and guides
Featured guides
Deep, human-written guides focused on accuracy, verification, and reproducible workflows.
Complex number guide
Rectangular and polar workflows.
Polar → rectangular
Convert r∠θ to a+jb.
Rectangular → polar
Magnitude/angle workflow.
Math hub
Tools + explainers across math topics.
FAQ
Do I use degrees or radians for θ?
Use whichever your workflow assumes, but be consistent and verify with known angles. If you’re unsure, convert explicitly.
How can I sanity-check the conversion?
Compute the magnitude √(a²+b²) and compare it to r (they should match up to rounding).
Tip: For reproducible work, save your inputs and reasoning in Notebook.