One way of thinking about imaginary numbers is to say that they are to negative numbers what negative numbers are to positive numbers. If we say "go east by -1 mile", it is the same as if we had said "go west by 1 mile". If we say "go east by i miles", it means the same thing as if we had said "go north by 1 mile". Similarly, if we say "go east by -i mile", it means the same as if we had said "go south by 1 mile".