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Complex Conjugate and Modulus Calculator — result sheet
Calculate the complex conjugate, modulus, and modulus squared of a+bi.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Conjugate=a−bi; modulus=√(a²+b²); modulus squared=a²+b².
The page shows the sign change in the imaginary component separately from the magnitude calculations.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Real part a — minimum -1000000000000; maximum 1000000000000
- Imaginary part b — minimum -1000000000000; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Real part a | 3 |
| Imaginary part b | 4 |
Conjugate =3−4i; modulus =5; modulus squared =25.
Assumptions and limits
- The input is a finite complex number represented by real coefficients.
- The modulus is the nonnegative Euclidean magnitude.
- Complex roots, arguments, 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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