How to use the complex number calculator
Find the modulus, argument and polar form of a complex number. Enter real part, imaginary part in the fields above; the modulus, argument, conjugate imaginary part are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “magnitude of complex number”, “polar form”, “conjugate”, “calculate complex number”, “find modulus”.
Formula
Variables
- re — Real part
- im — Imaginary part
Worked example
With real part = 3, imaginary part = 4, the calculator gives modulus ≈ 5 r; argument ≈ 53.1301 °; conjugate imaginary part ≈ -4.
Frequently asked questions
What is the complex number calculator used for?
Find the modulus, argument and polar form of a complex number. It helps with questions such as “magnitude of complex number”, “polar form”, “conjugate”.
What is the formula for the complex number calculation?
Modulus (r) = hypot(re,im). Argument (°) = atan2d(im,re). Conjugate imaginary part = -im. Here re is real part, im is imaginary part.
What inputs do I need for the complex number calculator?
You need real part, imaginary part. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the complex number calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the complex number result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.