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Complex Number to Rectangular Form Calculator — result sheet
Convert a complex magnitude and angle into real and imaginary rectangular components.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: a=r cosθ; b=r sinθ; z=a+bi.
The polar magnitude scales the unit direction defined by the angle. Converting the angle to radians before applying sine and cosine keeps the input contract explicit.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Magnitude r — minimum 0; maximum 1000000000
- Angle θ — degrees; minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Magnitude r | 5 |
| Angle θ | 53.130102354 |
Real part≈3; imaginary part≈4.
Assumptions and limits
- Magnitude is nonnegative and angle is measured in degrees.
- The output uses the standard positive-real, positive-imaginary Cartesian convention.
- No phase wrapping or signal normalization is applied beyond the ordinary sine and cosine functions.
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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