Complex Number Calculator

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

• Addition
• 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:

Complex Number Addition

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.

Complex Number Subtraction

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. 

Complex Number Multiplication

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 i² is equal to -1 so 22i² is 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.