What Happens to sin(i) for Complex i?

[schroder]

But now your distinction between "i" and "-i" depends upon which way is "up" and which way is "down", again an arbitrary choice.

It would be arbitrary if I was the first person to adopt this notation, but it is by now conventional that i is up and –i is down. In Electrical Engineering, j is up and represents inductive reactance and –j is down for capacitive reactance so it seems a convention is already established.

 

[rbj]

It would be arbitrary if I was the first person to adopt this notation, but it is by now conventional that i is up and –i is down. In Electrical Engineering, j is up and represents inductive reactance and –j is down for capacitive reactance so it seems a convention is already established.

but it doesn't matter. whether you call it "j" or "-j", other than the fact that they are negatives of each other, every property of these two imaginary numbers are precisely the same; they both square to be -1. if all math (and physics and electrical engineering) literature was changed and every occurance of i or j were replaced with -i or -j, every statement and every theorem would be just as valid as it was before. but you can't say that about replacing 1 with -1.

check out:

http://en.wikipedia.org/wiki/Imaginary_unit#i_and_.E2.88.92i

 

[schroder]

but it doesn't matter. whether you call it "j" or "-j", other than the fact that they are negatives of each other, every property of these two imaginary numbers are precisely the same; they both square to be -1. if all math (and physics and electrical engineering) literature was changed and every occurance of i or j were replaced with -i or -j, every statement and every theorem would be just as valid as it was before. but you can't say that about replacing 1 with -1.

All of that is true. The only point that I was making is that all ambiguity is removed by making a choice, and staying with that as a convention which has already been made in applied science and engineering. Then only in the realm of the pure mathematician does any ambiguity reside but that’s what pure mathematicians thrive on! I do not reside in that realm.

 

[Redbelly98]

... only in the realm of the pure mathematician does any ambiguity reside but that’s what pure mathematicians thrive on! I do not reside in that realm.

Nor do I.

The realm of pure mathematics is a nice place to visit, but I wouldn't want to work there.

 

[tiny-tim]

… don't talk to me about reality …

The realm of pure mathematics is a nice place to visit, but I wouldn't want to work there.

Mathematician to physicist:

Reality is a nice place to visit … but I wouldn't want to live there! ​

 

[hadi amiri 4]

WE know that sin(x)\leq1 but sin(i) is something else an anyone explain

 

[tiny-tim]

WE know that sin(x)\leq1 but sin(i) is something else an anyone explain

Haven't we already gone over this :

Hi hadi amiri 4!

… and so cosh(ix) = cos(x), sinh(ix) = i sinx,

and, conversely, cos(ix) = cosh(x), sin(ix) = -i sinx.

sin(A + iB) = sinA cosiB + cosA siniB = sinA coshB - i cosA sinhB.

cosh and sinh are known as hyperbolic cosine and sine.

sin(i) = sin (i.1) = -i sinh(1) = -i(e - 1/e)/2

 

[HallsofIvy]

WE know that sin(x)\leq1 but sin(i) is something else an anyone explain

We know that sin(x)\le 1 for real x. sin(z) for complex z is not bounded- it looks like an exponential along the imaginary axis. In fact, there is a famous theorem that if an entire function is bounded, it is constant.