Complex Number Calculator

Complex Number Calculator

The complex number calculator is used to evaluate the sum, difference, product, quotient, or the square root of two complex numbers with steps.

What is a complex number?

A Complex Number is a number that consists of a real number plus an imaginary number. A complex number is in the form a + bi. A Complex Number is calculated on the basis of multiplication, division, and the square root of the given number.

In the expression a+bi,

• "a" is called the real part
• "b" is the imaginary part of the complex number.

Complex numbers allow for solutions to certain equations that have no real solution. The advanced online Complex Number Calculator is used to calculate and find the complex number for a set of real numbers and an imaginary number.

Formula

Multiplication = (a+bi) × (a+bi)

Division = (a+bi) / (a+bi)

Square root:

• r = √ (a² + b²)
• y = √ ((r-a) / 2)
• x = b / 2y
• r₁ = x + yi
• r₂ = -x - yi

How to calculate the complex number?

The arithmetic operations can be performed on two or more complex numbers. 

Example:

Calculate the complex number for the given details.

1. Multiplication: (a+bi) × (c+di)

a = 10, bi = 2

c = 8, di = 2

Solution:

Apply Formula:

(a+bi) × (c+di)

Multiplication: (10+2) + (8+2)

Multiplication = 76   +   i*36

2. Division: [(a+bi) / (c+di)]

a = 15,    bi = 5
c = 10,    di = 5

Division = 1.4   +   i*-0.2

3. Square root: [ r₁ = x+yi ; r₂ = -x-yi]

a = 25   bi = 16

r₁ = 5.228845195610196   +  i* 1.5299745356233319
r₂ = -5.228845195610196   +  i* -1.5299745356233319