# Complex Number Calculator

Perform structured arithmetic and analysis for complex numbers in algebraic and polar form

> Canonical page: https://elysiatools.com/en/tools/complex-number-calculator

- **Category:** Math & Numbers

- **Keywords:** complex number, imaginary number, conjugate, modulus, argument, math

## Overview

The Complex Number Calculator is a specialized mathematical utility designed to perform arithmetic operations and structural analysis on complex numbers. Whether you need to add, subtract, multiply, divide, or calculate the conjugate, modulus, argument, or integer power of imaginary numbers, this tool delivers precise results in standard algebraic format.

## Inputs

- **Complex Number A** (text): e.g. 3+4i
- **Complex Number B** (text): e.g. 1-2i
- **Operation** (select)
- **Power Exponent** (number)
- **Decimal Places** (number)

## When to use

- When solving advanced algebraic equations that involve imaginary roots.
- When analyzing electrical engineering circuits using AC impedance calculations.
- When verifying manual math homework or academic research involving complex variables.

## How it works

- Enter your primary complex number (e.g., '3+4i') into the Complex Number A field.
- If performing a binary operation like addition or multiplication, enter a second value in the Complex Number B field.
- Select your desired mathematical operation from the dropdown menu, such as multiply, divide, modulus, or power.
- Adjust the decimal places or power exponent if needed, and run the calculation to receive the exact JSON output.

## Use cases

- Electrical engineering students calculating voltage, current, and impedance in alternating current (AC) circuits.
- Mathematicians and physicists performing vector rotations and 2D spatial transformations.
- Software developers writing test cases for math libraries that handle imaginary numbers.

## Frequently asked questions

### What format should I use to enter complex numbers?

Enter them in standard algebraic form, such as '3+4i' or '1-2i'. Ensure you include the 'i' to denote the imaginary part.

### Can I calculate the power of a complex number?

Yes, select the 'Integer Power' operation and specify an exponent between -12 and 12 in the Power Exponent field.

### What operations are supported?

The tool supports addition, subtraction, multiplication, division, conjugate, modulus, argument, and integer power calculations.

### How do I find the magnitude or angle of a complex number?

Use the 'Modulus' operation to find the magnitude (absolute value) and the 'Argument' operation to find the angle in radians.

### Can I control the precision of the output?

Yes, you can adjust the 'Decimal Places' setting to round your results to anywhere between 0 and 10 decimal places.

## Related tools

- [Mode Calculator](https://elysiatools.com/en/tools/mode-calculator): Find the most frequent value or values in a dataset and inspect the supporting frequency distribution
- [Prime Factorization Calculator](https://elysiatools.com/en/tools/prime-factorization): Factor any integer into its prime factors with detailed analysis and mathematical properties.
- [Perfect Number Checker](https://elysiatools.com/en/tools/perfect-number-checker): σ(n) = 2n ⟺ perfect. Factorization-based σ(n), proper-divisor sum, deficient/perfect/abundant classification, abundancy index, Euclid–Euler form. n ≤ 10¹².
- [Prime Number Checker](https://elysiatools.com/en/tools/prime-number-checker): Check if a number is prime (a natural number greater than 1 that has no positive divisors other than 1 and itself)
- [Wilson's Theorem Primality Checker](https://elysiatools.com/en/tools/wilson-theorem-checker): (n−1)! ≡ −1 (mod n) ⟺ n is prime. Exact factorial residue for n ≤ 10⁷, Miller–Rabin cross-check, composite factorial law, optional running-products trace.
- [ANOVA Calculator](https://elysiatools.com/en/tools/anova-calculator): Run one-way ANOVA across multiple groups and inspect sums of squares, F statistic, and p-value
- [Beam Reaction Force Calculator (Simply Supported)](https://elysiatools.com/en/tools/beam-reaction-force): Calculate support reactions of a simply supported beam via static equilibrium. UDL: RA=RB=q·L/2. Center point load: RA=RB=P/2. Off-center point load at a: RA=P·b/L, RB=P·a/L. Also returns max shear Vmax and max moment Mmax.
- [Combination Calculator](https://elysiatools.com/en/tools/combination-calculator): Calculate combinations (C(n,r)) with support for different types: with/without repetition, binomial coefficients, and detailed combinatorial analysis.

## Samples

- [EU VAT Number Samples](https://elysiatools.com/en/samples/eu-vat): Collection of EU VAT numbers from all member states for validation testing
- [Global Phone Number Samples](https://elysiatools.com/en/samples/global-phone): Collection of phone numbers from various countries for validation testing
- [Number & Currency Samples](https://elysiatools.com/en/samples/number-currency-samples): Text containing various number and currency formats for testing currency extraction
- [Passport Number Samples](https://elysiatools.com/en/samples/passport): Collection of valid passport number samples from various countries (China, USA, Japan, UK, Germany, etc.) for testing