why did we create numbers
I mugged up tables in school without actually knowing what they meant. I did the mathematical operations on numbers without actually knowing what I was doing.
Lets say why we had to create negative numbers?
I could relate the answer to the daily problem in trading world. Person A borrows X units of money from B and so person A has -X money. And hence all the math in the money trade becomes easier.
Why did we have to create "i" - the complex number?
X^2 - 1 = 0 is a second order equation and it has clearly two roots
X = 1 and X = -1..
but how about X^2+1 = 0 ... we come up with a number "i" and say X = +i and X = -i are the two roots.
If we get back to the conceptual level it is basically X =1 and X = -1 on the imaginary line. Why did we have to have an imaginary line. It is because we would like to describe two systems (one corresponding to real axis and other to imaginary axis) at the same time.
That is when we write e^(jx) = cos(x) + i sin (x)... we would like to analyse cos(x) and sin(x) at the same time. in other words we would like to analyze the property of a general sinusoid signal measuring its phase from a cosine of same frequency and sine of the same frequency. [remember any sinusoid can be perfectly reconstructed if we know the amplitude, frequency and phase]
*********************************
more on the number "e" in the future posts.
Lets say why we had to create negative numbers?
I could relate the answer to the daily problem in trading world. Person A borrows X units of money from B and so person A has -X money. And hence all the math in the money trade becomes easier.
Why did we have to create "i" - the complex number?
X^2 - 1 = 0 is a second order equation and it has clearly two roots
X = 1 and X = -1..
but how about X^2+1 = 0 ... we come up with a number "i" and say X = +i and X = -i are the two roots.
If we get back to the conceptual level it is basically X =1 and X = -1 on the imaginary line. Why did we have to have an imaginary line. It is because we would like to describe two systems (one corresponding to real axis and other to imaginary axis) at the same time.
That is when we write e^(jx) = cos(x) + i sin (x)... we would like to analyse cos(x) and sin(x) at the same time. in other words we would like to analyze the property of a general sinusoid signal measuring its phase from a cosine of same frequency and sine of the same frequency. [remember any sinusoid can be perfectly reconstructed if we know the amplitude, frequency and phase]
*********************************
more on the number "e" in the future posts.
posted by Pilli at 1:41 PM
4 comments
