# Complex Number Calculator Complex Number is a number that consists of a real number plus an imaginary number. Complex Number is in the form a + bi. Complex Number is calculated on the basis of multiplication, division and square root of the given number. In the expression a+bi, a is called the real part and b the imaginary part of the complex number.
Complex Number
 Multiplication: [ (a+bi) × (a+bi) ] a: bi: a: bi: Multiplication: Division: [ (a+bi) / (a+bi) ] a: bi: a: bi: Division: Square root: [ r1 = x+yi ; r2 = -x-yi ] a: bi: r1: r2:
Formula
Multiplication = (a+bi) × (a+bi)
Division = (a+bi) / (a+bi)
Square root: r = sqrt(a² + b²) y = sqrt((r-a) / 2) x = b / 2y r1 = x + yi r2 = -x - yi
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 set of real number and an imaginary number.

Example:
Calculate the complex number for the given details.
1. Multiplication: (a+bi) × (a+bi) ]
a = 10 bi = 2
a = 8 bi = 2

Solution:
Apply Formula:
(a+bi) × (a+bi)
Multiplication: (10+2) + (8+2)

Multiplication = 76   +   i*36
2. Division: [ (a+bi) / (a+bi) ]
a = 15    bi = 5
a = 10    bi = 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
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