COMPLEX NUMBERS SIMPLY EXPLAINED WITH PURPOSE AND APPLICATIONS
COMPLEX NUMBERS SIMPLY EXPLAINED WITH PURPOSE AND APPLICATIONS.
|||| Complex number indicate inclination almost always.
|||| Example 1
Imagine you opened a picture in microsoft paint.
Now lets say you rotated that image by 90 degrees. That is "i".
i = inclination by 90 degrees.
i * i = inclination by 180 degrees.
i*i*i = inclination by 270 degrees.
i*i*i*i= inclination by 360 degrees.
and so on.
Why is complex numbers a part of maths?
A normal number line can be used to denote an increase or a decrease in length or distance or area etc.
||||However, can such a line help you when the object has just been rotated or inclined at an angle?
|||| This where the complex plane comes into picture. It is used to measure how much you are inclining the object.
WHAT ABOUT NUMBERS LIKE 3+4i?
|||| Is it necessary that an object should be inclined by 90 degree or 180 degree or 270 degree sharp?
|||| Cant it be inclined at a lesser or an intermediate angle.
|||| If you take tan inverse of 3 + 4i, you will get the angle by which it is inclined.
|||| 3 is the view you will get if you stands upon the x-axis and look upwards towards the object (i.e the top view)
|||| 4 is the view one will get if climb up the Y-axis like climbing up a pole and then try to view that object (i.e 4 is the front view of the object)
|||| Now what is the actual length of the object?
|||| It can be found by sqrt(3*3 + 4 *4).
WHAT DOES THE COMPLEX PLANE LOOK LIKE?
|||| In many ways it looks like a map having NORTH, SOUTH and EAST, WEST arrows.
|||| The only difference : Instead of North-South, there is i and -i.
|||| And instead of East-West, there is 1 and -1.
|||| Now let's say that you are standing facing towards the East. This is like going towards i on a complex plane and so on.
|||| Comparing these two planes, we can say the...