Imaginary Number Calculator

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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