Maybe i should just stick to maths.
Woah.. after listening to a lot of nonsence after my previous post i guess maths is the most logical thing to talk about! Well today i shall talk about something abstract.
Now who here knows what a complex number.. or maybe an imginary number..
"wad is an imaginary number??" "how can a number be imaginary?" i bet those are the questions running in your mind.
well here is how my prof explained it to me.
accept that since square root of -1 cannot exist in the real world(real numbers). Then it must exist somewhere. now lets call the magical value i(only the positive part).
So now imagine a graph where the x axis is the real numbers and the y axis is the imaginary axis. ie the numbers in the imaginary axis go ...3i,2i,i,0,-i,-2i,-3i... and the x axis is the normal real axis ie ...-3,-2,-1,0,1,2,3...
now the to find the square root of ab we can find the root of a then root of b and multiply.
so now lets say we want to know the square root of -4 it is the same as the square root of 4=2 times the square root of -1=i
so we get the magical result sqrt of -4= 2i
now think about the coordinate (1,2) it represents a special number namely the number 1+2i or generalising i can say that (a,b) reprisents a+bi
ok so thats that.
now look at the a+bi note that taking the distance from the origin to the point will give us sqrt (a^2+b^2). thus let the angle formed between the line and the positive x axis be p rad.
thus we can write a+bi as sqrt(a^2+b^2)*(cos p +isin p) since cos p=a/sqrt(a^2+b^2), sin p=b/sqrt(a^2+b^2)
now here is the best part.
we have a short form for writing the expression sqrt(a^2+b^2)*(cos p +isin p) we simply write sqrt(a^2+b^2)*e^(ip).
for a proof of this look at the maclaurens series it converges beautifully
now for the most magical part of this whole lesson!!
look at the number e^(i*pi) now notice that if pi is the angle formed, then we are back on the real axis so we have the magical number e^(i*pi)=-1.
Wow!
I just combined three of the most beautiful numbers ever discovered to make it more magical, we can say that e^(i*pi)+1=0 now every part of that is magical. all the five numbers are special.
pls message or ask me if you need any clarifications.