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Complex Number Arithmetic — result sheet
Adds, subtracts, multiplies, or divides two complex numbers and reports the magnitude.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: (a+bi) op (c+di); magnitude |z| = sqrt(re^2 + im^2).
Combine real and imaginary parts per the operation; division uses the conjugate over c^2 + d^2. Magnitude is the distance from the origin.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Real part of first number — minimum -1000000000; maximum 1000000000
- Imaginary part of first number — minimum -1000000000; maximum 1000000000
- Real part of second number — minimum -1000000000; maximum 1000000000
- Imaginary part of second number — minimum -1000000000; maximum 1000000000
- Operation — 4 choices
Worked example
| Input | Value |
|---|---|
| Real part of first number | 3 |
| Imaginary part of first number | 2 |
| Real part of second number | 1 |
| Imaginary part of second number | 4 |
| Operation | add |
Result 4+6i; magnitude 7.2111.
Assumptions and limits
- Finite real and imaginary parts.
- Division requires a nonzero-modulus divisor.
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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