Originally posted by bobbob1056thI am also intrigued by the number i. A good way to visualize any complex number A + Bi, where A and B are both real, is to set-up the 'complex plane' where A is plotted on the x-axis, and B is plotted on the y-axis. Then any point (A,B) on the complex plane corresponds to the complex number A + Bi. Additionally, if you draw a vector from the origin of the plane to this point (A,B), then this vector is also a very useful construct. The magnitude of the vector is just (A^2 + B^2)^0.5, and the angle the vector makes with the x-axis is InverseTan(B/A). Thus this is a vector representation of the number A + Bi.
I have often been intrigued by the concept of the number i. It is not part of the negative, positive, limitless/irrational, or nuetral numbers. Therefore I see it as a different root from 0 (there is 0, then there are the positive numbers, the negative numbers, (both which root from 0 (ie 0 is the limit))and then there's i and similar number groups). ...[text shortened]... is very peculiar about mathematics? I realize the thread name isn't very accurate... oh well.
Originally posted by davegageAlong those lines, another strange result from Euler's formula is the following:
I am also intrigued by the number i. A good way to visualize any complex number A + Bi, where A and B are both real, is to set-up the 'complex plane' where A is plotted on the x-axis, and B is plotted on the y-axis. Then any point (A,B) on the complex plane corresponds to the complex number A + Bi. Additionally, if you draw a vector from the origin of ...[text shortened]... s actually purely real and is just exp(-Pi/2) = 0.2078795764....... Very peculiar results IMO.
Originally posted by nickhawkerI think "i" is a bit of a weird number. I'm not 100% positive, but I'm pretty sure it was invented to solve an equation involving the square root of -1. Before "i", that equation didn't make sense. "i" was like a big mathematical band-aid, almost a cheat in a sense.
I wouldn't say "i" is any more strange than a negative number considering that both are equally imaginary as neither actually exist, both are just tools invented for maths. Zero is a bit odd too really...
Originally posted by orfeoThat reminds me of a joke I saw somewhere (might have been here at RHP).
i is by definition an 'imaginary' number, useful for solving certain kinds of equations.
I don't why on earth one of the posters thinks that NEGATIVE numbers don't exist, though.
Originally posted by bobbob1056thActually, real functions are much harder to study than complex functions (= functions defined on the complex plane).
But functions with i and "normal" numbers are much stranger than functions with negative numbers, or zero, and "normal" numbers.
Originally posted by AlcraIt's true. I've seen it happen.
Two men, one of which happens to be a mathematician, are sitting in a park, watching a house across the road. At some point, someone enters the house, and a few minutes later, two people leave. Says the mathematician, "If another person should now enter the house, it will be empty."