Calculator Inputs
Formula Used
For a complex number z = a + bi, the modulus measures the distance from the origin on the complex plane.
The calculator squares the real part, squares the imaginary part, adds both values, and then takes the square root.
How to Use This Calculator
- Enter the real part of the complex number.
- Enter the imaginary coefficient without the letter i.
- Choose the output precision you want.
- Enable detailed steps if you want the working shown.
- Optionally paste multiple complex numbers for batch comparison.
- Press Calculate Modulus to display the result above the form.
Example Data Table
| Input | Real Part | Imaginary Part | Modulus | Argument (Degrees) |
|---|---|---|---|---|
| 3+4i | 3 | 4 | 5 | 53.1301 |
| 5-12i | 5 | -12 | 13 | -67.3801 |
| -7+24i | -7 | 24 | 25 | 106.2602 |
FAQs
1. What is the modulus of a complex number?
It is the distance from the origin to the point representing the complex number on the complex plane. It is always non-negative.
2. Why does the formula use a square root?
The modulus follows the Pythagorean theorem. The real and imaginary parts form perpendicular sides, so the modulus becomes the hypotenuse.
3. What happens if the imaginary part is zero?
The complex number lies on the real axis, and the modulus becomes the absolute value of the real part.
4. Can this tool show polar information too?
Yes. It reports the argument in radians and degrees, plus polar and exponential forms for the same complex number.
5. What is modulus squared useful for?
It is often used in algebra, signal analysis, and proofs because it avoids the square root while preserving magnitude information.
6. Can I evaluate several numbers together?
Yes. Paste one complex number per line in the batch box to build a comparison table automatically.
7. Why is the argument negative sometimes?
Angles below the real axis are often expressed as negative values. This is normal and depends on the quadrant.
8. Do the export buttons save the result table?
Yes. CSV exports structured values, while PDF captures the visible result summary for sharing or printing.