Calculator
What the Complex Number Calculator does
Complex Number Calculator: calculates Modulus |z|, Argument (°) and Conjugate from Real part a and Imag part b. Example: real part a 3 and imag part b 4 gives modulus |z| 5.000000.
The Complex Number Calculator turns Real part a and Imag part b into Modulus |z|, Argument (°) and Conjugate. Change any input and the output follows immediately.
The method matters as much as the answer when you are still learning the topic. That is usually what brings someone sanity-checking a spreadsheet here.
The work is done by JavaScript already loaded in your browser, so your input never crosses the network.
Everything needed to verify a result is further down: the fields, the method and one fully worked example.
What do the Complex Number Calculator fields mean?
The Complex Number Calculator uses 2 inputs. None of the boxes start empty. The page loads with a worked set of values you can edit or replace.
| Field | What to enter | Default |
|---|---|---|
| Real part a | required | 3 |
| Imag part b | required | 4 |
How does the Complex Number Calculator work?
Each output is derived from the inputs above in a single pass; there is no hidden state carried between runs, so the same inputs always give the same calculation.
Bad input produces an error, never a confident-looking wrong answer.
Worked example
These are the values the Complex Number Calculator loads by default, and the result it produces from them. Open the tool above and you will find precisely these figures already in place.
| Real part a | 3 |
|---|---|
| Imag part b | 4 |
| Modulus |z| | 5.000000 |
|---|---|
| Argument (°) | 53.1301 |
| Conjugate | 3 − 4i |
| What this means | |z| = 5, arg ≈ 53.13° |
How to use it
- Key in Real part a.
- Fill in Imag part b.
- There is nothing to click. The answer keeps pace with your edits.
- Read Modulus |z|, Argument (°), Conjugate and What this means in the results panel.
- Use Copy Link if you want the same setup again later, or Print for a paper copy.
What this tool does not do
- Very large or very small numbers hit JavaScript floating-point limits (about 15 significant digits).
- Displayed values are rounded; the underlying calculation keeps full precision.
- It handles the common case well and the unusual case literally.
Frequently asked questions
You need Real part a and Imag part b. Each field is pre-filled with a sensible default, so nothing is mandatory before you see a result.
With the values loaded when the page opens, modulus |z| comes out as 5.000000. Nudge one field at a time to see which one the answer is most sensitive to.
It never leaves the tab. The page does the work itself rather than asking a server to.
Free for any use, personal or commercial.
The computation is exact; how much you should trust the answer depends on how good your inputs are.