# Complex Number Calculator

Perform different functions on complex numbers by entering values of variables in the complex number calculator.

Formula:

a
bi

a
bi

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This complex number calculator (imaginary number calculator) can perform multiple mathematical operations on complex numbers like:

• Subtraction
• Multiplication
• Division
• Roots

## What are Complex Numbers?

Complex numbers are mathematical pairs of real (without iota) and imaginary (with iota) numbers. They are normally represented through the notation.

z = a + bi

Knowledge of complex numbers is required in many scientific fields like electromagnetism, quantum physics e.t.c.

## Arithmetical Operations on Complex Numbers

Different arithmetical operations can be performed on complex numbers easily. The real part of the complex numbers reacts with a real part and the imaginary part reacts with the imaginary part.

The Iota of the complex numbers is neglected during some operations. Some examples are given below:

Example

Add the complex numbers 7 + 5i and 3 + 2i.

Solution

Identify and separate the real and imaginary parts and write them under each other.

Real part (a)                    imaginary part (bi)

7                                         5

+          3                                         2

______________________________

10                                        7

The resulting complex number is 10 + 7i.

### Example

Subtract the complex number 2 + 7i from 5 + 9i.

Solution

Identify and separate the real and imaginary parts and write them under each other.

Real part (a)                    imaginary part (bi)

5                                           9

-   2                                           7

_____________________________

3                                           2

The resulting complex number is 3 + 2i

### Example

Multiply the complex number 5 + 11i from 2 + 2i.

Solution

= (5 + 11i )*(2 + 2i)

= 5 (2 + 2i) + 11i (2 + 2i)

= 10 + 10i + 22i + 22i2                    (as iis equal to -1 so 22iis equal to -22)

= 10 - 22 + 10i + 22i

= -12 + 32i.

The resulting complex number is -12 + 32i

Note: Don’t forget to enter the "-" sign with the values. For example, if a complex number is 5 - 2i, enter -2 as the imaginary value.