# Complex Number

## Complex Number

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...