Why not call them "identities"? A set of numbers is just a set if symbols. A set of symbols, is just a set of unique identities. Identities (points) are irrational to a 1 dimensional number line. Therefore, "identities" are irrational.
A function could be seen as a kind of mapping. If you take y = 2x you could think of it as a kind of mapping because you "map" every number to its double. But I would say a mapping usually has some boundaries, like mapping every number betweeen 0 and 1 to every number between 0 and 100.
So... You basically introduced i with a different variable and then went on and explained how a cartesian coordinate system can be converted to polar and the quickly wrote down this 'eulers formula'. I don't get how that is of any use when calculating imaginary numbers...
yeah, it seems that the formula isn't useful at all if we have no value for r or theta, since then we only know what e & i are. BUT, if we know any complex values, say, -3+7i, then we can convert it to Euler's. Still trying to figure this out myself.
The square root of 2 is an irrational number when you have a unit length of 1 on the x and y plane. Therefore r is irrational. But if r = 1 then you have to have an irrational value somewhere else. So "e" serves as that irrational value when r wants to be a real number. Therefore when r = 1, the identity of point z is called "r*e^j*theta". So we can't "calculate" imaginary numbers, we can only "name" them, and then shift these names around in algebra. This helps us understand if some imaginary number is "equal" to another through correspondence, even if we don't get any numeric value from it. If you can think of the square root of -1 as simply "identity", then you can understand why we can't assign a number to it. Because all the numbers are used on the 1 dimensional line that progresses to infinity. We can't use them to represent "identities" except by calling them i*theta or j*theta etc.
Gauss called Imaginary Numbers "Lateral Numbers," because he thought of them as existing "along with" Real Numbers.
Lateral! I wish I knew that back in 7th grade algebra. The term 'imaginary' does so much harm.
Why not call them "identities"?
A set of numbers is just a set if symbols.
A set of symbols, is just a set of unique identities.
Identities (points) are irrational to a 1 dimensional number line. Therefore, "identities" are irrational.
Thanx ! Really knocked off some of my "rust"!😂
Thank you very much a nice and useful
It's not usual for it to be j, i is the typical notation for sqrt(-1). Good to know the options though.
Please Sir, I want to know
?Is there any difference between mapping and function
A function could be seen as a kind of mapping. If you take y = 2x you could think of it as a kind of mapping because you "map" every number to its double. But I would say a mapping usually has some boundaries, like mapping every number betweeen 0 and 1 to every number between 0 and 100.
So... You basically introduced i with a different variable and then went on and explained how a cartesian coordinate system can be converted to polar and the quickly wrote down this 'eulers formula'. I don't get how that is of any use when calculating imaginary numbers...
yeah, it seems that the formula isn't useful at all if we have no value for r or theta, since then we only know what e & i are. BUT, if we know any complex values, say, -3+7i, then we can convert it to Euler's. Still trying to figure this out myself.
The square root of 2 is an irrational number when you have a unit length of 1 on the x and y plane. Therefore r is irrational.
But if r = 1 then you have to have an irrational value somewhere else. So "e" serves as that irrational value when r wants to be a real number.
Therefore when r = 1, the identity of point z is called "r*e^j*theta".
So we can't "calculate" imaginary numbers, we can only "name" them, and then shift these names around in algebra.
This helps us understand if some imaginary number is "equal" to another through correspondence, even if we don't get any numeric value from it.
If you can think of the square root of -1 as simply "identity", then you can understand why we can't assign a number to it. Because all the numbers are used on the 1 dimensional line that progresses to infinity. We can't use them to represent "identities" except by calling them i*theta or j*theta etc.
I don't get it. Why is 1024 a COMPLEX number but -44.1 a REAL number?
What if I told you both of them are real and complex numbers at the same time. It is just so happens that their imaginary part is equal to 0.
Not bad but i would stick with i not j, as j,k,l is used in hypercomplex numbers when using complex numbers in higher dimensions.
in electrical engineering we usually use j. Also called as j operator.
Problem in Electrical Engineering is that i is the symbol for current so they decide to use j