Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org

# Complex numbers arithmetic

This solver can performs basic operations with complex numbers i.e., addition, subtraction, multiplication and division. Step-by-step explanations are provided.

Arithmetic operations with complex numbers
0 1 2 3 4 5 6 7 8 9 - / . del
Show me an explanation
example 1:
$$\left( 2 - 4i \right) \color{red}{+} \left(5 + 3i\right)$$
example 2:
$$\left( \frac{1}{2} - 2i \right) \color{red}{\cdot} \left(\frac{5}{2} - \frac{6}{5}i\right)$$
example 3:
$$\frac{4-6i}{1+i}$$
example 4:
$$\left( \frac{7}{2} - 2i \right) \color{red}{-} \left(\frac{5}{2} + 3i\right)$$

## About operations on complex numbers

A complex numbers are of the form , a+bi where a is called the real part and bi is called the imaginary part. This text will show you how to perform four basic operations (Addition, Subtraction, Multiplication and Division):

Example: let the first number be 2 - 5i and the second be -3 + 8i. The sum is:

(2 - 5i) + (- 3 + 8i) = = ( 2 - 3 ) + ( -5 + 8 ) i = - 1 + 3 i

### Subtraction:

Subtract the real parts and subtract the imaginary parts.

Example: let the first number be -3 + 7i and the second be 6 - 9i. The sum is:

(- 3 + 7i) - (6 - 9i) = = ( - 3 - 6 ) + ( 7 - ( -9 ) ) i = - 9 + 16 i

### Multiplication

To multiply complex method use the FOIL method( First, Outside, Inside, and Last. )

Example: multiply 3 + 4i and 2 - 6i

First terms: 3 * 2 = 6

Outside terms: 3 * (- 6i) = -18i

Inside terms: 4i * 2 = 8i

Last terms: 4i * (-6i) = -24 * i2 = -24 (- 1) = 24

Now, combine everything together

6 - 18i + 8i + 24 = 30 - 10i.

### Division

Multiply both the denominator and the numerator by the conjugate of the denominator

Example: divide 2 + 3i and 4 - 5i

Quick Calculator Search