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Complex Number Rectangular-Form Calculator — result sheet
Calculate rectangular real and imaginary components from a complex magnitude and argument.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: a=r cos(θ); b=r sin(θ); complex number=a+bi.
The calculator converts polar-style magnitude and angle into the rectangular coefficients used by a+bi notation.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Magnitude r — minimum 0; maximum 1000000000000
- Argument — minimum -1000000000000; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Magnitude r | 5 |
| Argument | 53.1301023542 |
a≈3; b≈4; complex number ≈3+4i.
Assumptions and limits
- Angle is entered in degrees and converted to radians.
- The magnitude is nonnegative and the result uses the principal rectangular components.
- Branch selection and symbolic simplification are not modeled.
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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