Arithmetic Course/Types of Number/Imaginary Number

Imaginary Number
Imaginary Number is defined as
 * $$i = \sqrt{-1}$$

Addition

 * i + 0 = i
 * i + i = 2i
 * i + (-i) = 0

Subtraction

 * i - 0 = i
 * i - i = 0
 * i - (-i) = 2i

Multiplication

 * i x 0 = 0
 * i x i = i2 = -1
 * i x (-i) = -i2 = 1

Division

 * i / 0 = Error
 * i / i = 1
 * i / (-i) = -1