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Utilnivo

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Utilnivo

Complex Number Calculator

Work with rectangular, polar, and exponential complex forms locally.

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  • On your device

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Private on your device

Your information stays on your device and is not uploaded.

Related tools

Enter complex numbers like 3+4i to inspect magnitude, argument, conjugate, and alternate formats. Add, subtract, multiply, and divide complex values with clear validation and local processing.

Utilnivo’s Complex Number Calculator helps learners move fluently between rectangular, polar, and exponential forms. Enter a+bi once, then inspect magnitude, argument, conjugate, and formatted alternatives.

Arithmetic operations stay explicit and local. Multiplication and division follow the standard algebraic identities, while polar power and root helpers are available through the shared complex module when needed.

The imaginary unit is treated distinctly from variables so expression editors do not confuse i with an unknown. Clear validation messages explain malformed inputs such as missing operators between real and imaginary parts.

Because everything runs in the browser, you can practice complex arithmetic for coursework or engineering checks without uploading values. Pair this tool with the Matrix Calculator when complex linear algebra is required later.

How to use this tool

Type a value such as 3+4i. Review magnitude, argument, conjugate, and alternate forms. Optionally enter a second operand and choose an arithmetic operation. Switch the display format without changing the underlying value.

Worked example

For 3+4i the magnitude is 5 and the conjugate is 3-4i. Polar form uses r=5 and θ=atan2(4,3).

When to use this

  • Converting homework answers between rectangular and polar form.
  • Checking complex multiplication and division by hand.
  • Inspecting magnitude and argument quickly.

Common examples

  • 3+4i
  • 1+i
  • polar form
  • complex conjugate

Common mistakes

  • Writing the imaginary unit as a variable x instead of i.
  • Forgetting that argument depends on quadrant (use atan2).
  • Dividing by zero when both real and imaginary parts are zero.

How it works

Enter a complex number in a+bi form. Utilnivo converts between rectangular, polar, and exponential representations and can add, subtract, multiply, or divide two complex values locally.

Limitations

Results are based on the inputs you provide and may not cover every edge case. This tool is for general use and is not professional advice.

Privacy and file handling

Your data stays on your device and is not uploaded.

Formula or method

Rectangular arithmetic uses (a+bi)(c+di)=(ac-bd)+(ad+bc)i. Polar conversion uses r=√(a²+b²) and θ=atan2(b,a). Division multiplies by the conjugate of the denominator.

FAQ

Frequently asked questions

What formats are supported?

Rectangular a+bi, polar magnitude and argument, and exponential form are available.

How do I enter a complex number?

Use forms such as 3+4i, -2+0.5i, or a pure imaginary value like 2i.

Is the imaginary unit treated as a variable?

No. The calculator treats i as the imaginary unit, distinct from ordinary variables.

Related pages

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