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.
I feel, the classical description of the line with respect to a circle (cuts at two points; touched at one point as a tangent; does not cut) is easier to understand thanks to the geometrical intution (we have a better intuitive feel for geometry than for algebra). Of course an algebraic description (using complex numbers) has its merits (it is more generic) but seems a bit heavy for young school kids.
ReplyDeleteHow do you interpret the sin(x)= 2,please clarify, my interest is to know whether the line y=2 is a tangent to y= sin(x)
ReplyDeletethe post refers to solution of a quadratic equation and a linear equation.....
ReplyDeleteinteresting pl answer rightly
ReplyDelete