A note on Imaginary points in Coordinate Geometry

The young school boys begin elementary arithmetic where they deal with positive numbers. When introduced to negative numbers they find it difficult  to accommodate. Even mathematicians of high repute, in olden days,  regarded negative roots of an algebraic equation as false roots.

The difficulty of the beginner in understanding the meaning of          

is same as that of the young school boy.

It is unfortunate that numbers involvingare called imaginary numbers;since it gives a wrong impression to the beginner that these numbers do not exist. In fact the so called imaginary numbers are of great use in certain branches of pure and applied mathematics.

In the context of coordinate geometry, the issue of dealing with imaginary numbers is tricky for the point with imaginary coordinates cannot be shown in a diagram/figure; yet we use them...

For example, consider a circle x²+y² = 4 and the line x = 4. Here we have two situations of describing the position of the line with respect to the circle:

·        -- One way to comprehend is that, given a line and a circle, the line cuts the circle at two points or the line touches the circle at one point and is a tangent to the circle or the line does not touch the circle.

·        -- The other way is to say that the line always meets the circle at two points.