You are here:

# Calculators :: Complex numbers :: Operations with one complex number

This calculator extracts the square root, calculate the modulus, finds inverse, finds conjugate
and transform complex number to polar form. The calculator will generate a detailed explanation for
each operation.

## Polynomial Calculators

Find Roots, Factor, Expand, Simplify, Graph,...

##
Rational Expressions

Simplify, Multiply, Divide, Add, Subtract

## Radical expressions

Rationalize, Simplify

## Solving Equations

Solve Quadratic, Polynomial or Rational Equation

## Quadratic equation

Solving, Factoring, Graphing,...

## Plane Geometry

Triangle, Sine/Cosine Law, Square, Rectangle

## Complex numbers

Operations, Polar Form, Simplifying, Inverse,...

## Systems of equations

Systems 2x2, 3x3 and 4x4

## Vectors and Matrices

2D/3D Vectors, Matrix Determinant & Inverse

## Calculus Calculators

Limits, Derivatives, Integrals

## Sequences Calculators

Arithmetic, Geometric

## Analytic Geometry

Line, Triangle, Circle,...

## Trigonometry Calculators

Degrees, Radians, Equations

## Numbers

Fractions, LCM, GCD, Prime Numbers,Percentages...

## Statistics Calculators

Descriptive, Dispersion, Normal Dist., Regression,..

## Financial Calculators

Simple-Compound Interest, Amortization, Annuity

## Other Calculators

Sets, Work Problems

## Formulas for conjugate, modulus, inverse, polar form and roots

### Conjugate

The conjugate of the complex number * z = a + bi * is:

**Example 1: **

**Example 2: **

**Example 3: **

### Modulus (absolute value)

The absolute value of the complex number * z = a + bi * is:

**Example 1: **

**Example 2: **

**Example 3: **

### Inverse

The inverse of the complex number * z = a + bi * is:

**Example 1: **

48 861 664 solved problems