Imaginary Number Calculator

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Imaginary numbers are usually represented by 'i'. An imaginary number can be written as a real number when multiplied by another imaginary number by the basic formula i2 = -1. Different mathematical operations are used to solve imaginary numbers.The online tool used to calculate the imaginary number is called as Imaginary number calculator.


Example 1: Expand the given expression with imaginary number: (2i-3)2

The given question is (2i - 3)2

The first step is to expand the given expression.

(2i - 3)2 = (2i - 3) (2i - 3) = (2i) 2 + 2(2i)(-3) + (-3)2

 4i2 - 12i + 9

This expression can be further simplified by the property i2 = -1.

4i2 - 12i + 9 = 4(-1) -12i + 9 = -4 +9 -12i = 5 -12i

Hence > (2i - 3)2 = 5 -12i.



Example 2: Expand the given expression with imaginary number: (i - 5) (4i - 1)

The first step is to multiply the given expression.

(i - 5) (4i - 1) = i(4i) +i(-1) -5(4i) +5

= 4i2 -20i -i +5 = 4i2 -21i + 5

This expression can be further simplified by the property i2 = -1.

4i2 -21i +5 = 4(-1) -21i +5 = -20i +1. 

Hence > (i - 5) (4i - 1) = 1 -20i.


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