i used a taylor expansion of the sine function to calculate the sine of the imaginary unit 'i', to get 1.175i. is this correct? thanks.

The definition of sin x is:

\sin x = \frac{e^{ix} - e^{-ix}}{2i}

Plugging in x=i, we get

\sin i = \frac{e^{-1} - e^{1}}{2i} = (e/2 - 1/2e)i = (1.1752011...)i

So, it seems you are correct.

http://upload.wikimedia.org/math/5/d/3/5d32785481dec2be0c115f510f164dd1.png

So

sin(i) = i + \frac{i}{3!}\ + \frac{i}{5!}\ - \frac{i}{7!}\ ...

sin(i) = i + 0.166666667i + 0.00833333333i - 0.000198412698i ...

sin(i) \approx 1.175i

So yes, you are correct.

Dont you just love Taylor expansions:)

thanks guys. i tried checking with my TI-83 calculator, but it wouldn't give me an answer. i even have it set to 'a +bi' in the mode section instead of 'real'.

i used a taylor expansion of the sine function to calculate the sine of the imaginary unit 'i', to get 1.175i. is this correct? thanks.
i don't really know why but i keep seeing -90 degrees at right angles to the sine in question.

is that correct guys?

Oh shit, here we go again with this stuff, if I could only understand...why don't you explain this. :D

The definition of sin x is:

\sin x = \frac{e^{ix} - e^{-ix}}{2i}

Plugging in x=i, we get

\sin i = \frac{e^{-1} - e^{1}}{2i} = (e/2 - 1/2e)i = (1.1752011...)i

So, it seems you are correct.

neat. i've never seen that indentity before.

Learn it and love it---when you take a complex analysis class, you'll need it all the time for evaluating integrals.

they teach a little about it in electrical engineering classes too.

Oh shit, here we go again with this stuff, if I could only understand...why don't you explain this. :D

is it too complex for you? ;) :D (just thought i'd inject some math humor into the thread.)

The definition of sin x is:

\sin x = \frac{e^{ix} - e^{-ix}}{2i}

Plugging in x=i, we get

\sin i = \frac{e^{-1} - e^{1}}{2i} = (e/2 - 1/2e)i = (1.1752011...)i

So, it seems you are correct.


Why do I get -1.175... Sure you have the sines on the identity right?
Maybe I'm just tired.

kevinalm:

You're probably forgetting that

\frac{1}{i} = -i,

which follows directly from

i^2 = -1

(divide both sides by -i).

Yep, that would be it. Thanks.

is it too complex for you? ;) :D (just thought i'd inject some math humor into the thread.)

Its not to complex , its that I just do not understand it. If I could learn what you are figuring out, I could then enjoy the humor as much as you seem to.

cosmictraveller, numbers like 2 + 3i with a real part (2) and an imaginary part (3i, where i=squareroot(-1)) are called 'complex numbers'. That was the joke. ;)

Thank you for that explanation, I think I understand a little better now.

don't really know why but i keep seeing -90 degrees at right angles to the sine in question.

is that correct guys? Hmmm. Are you mentally graphing i - picking the point (0,i) on the complex plane - and looking at the angle from the horizontal as 90 ?

If so, that would be different from the matter here, which would be sort of an "i distance" along the circumference of the "i unit circle" (lightning has not struck me, for writing that).

Check out the sine of 1, for example.

There was a mathematician who attempted something like that in the eighteenth century. I forgot his name, but he was trying to calculate the area of a 1-sphere using i in the radius... forgot what became of that...

they teach a little about it in electrical engineering classes too.They have to. The equations for electronic circuits are full of imaginary numbers. They use hyperbolic trigonometry and all that stuff. Electrical engineering really blurs the boundary between math and physics. In my dad's day electrical engineers used j as the symbol for -1^.5 . I think the standardization on i to conform to the usage of other disciplines occurred in the 1950s. By the time I started studying it in the 1960s it was i.Hmmm. Are you mentally graphing i - picking the point (0,i) on the complex plane - and looking at the angle from the horizontal as 90 ? If so, that would be different from the matter here, which would be sort of an "i distance" along the circumference of the "i unit circle" (lightning has not struck me, for writing that).Yes. You have to be careful which "universe" you're working in. The angle between the real axis and the imaginary axis in the complex plane is not the same as the angle between the two sides of a sector covering one-fourth of a circle of radius i. That circle does not lie on the complex plane, it exists in an imaginary universe, if you will.

If you plug an imaginary or complex value into a formula which is defined only for arguments of absolute value (such as A = pi r^2), it's just as risky as plugging in a negative value.There was a mathematician who attempted something like that in the eighteenth century. I forgot his name, but he was trying to calculate the area of a 1-sphere using i in the radius... forgot what became of that...Same problem. The radius of a sphere is the distance between its center and any point on its surface. By definition that is an absolute value. Defining the radius as something outside that range transports you into an imaginary universe where the formulas may be different.

You'll have the same problem if you attempt to predict the behavior of the molecules in matter cooled to -1 degree Kelvin. Temperature is an absolute value.

I tell cosmologists they should treat time the same way. It is an absolute number, with 0 at the Big Bang. There is no "before the Big Bang." They can study the events in those first femtoseconds in more detail by graphing time on a log scale, which puts the Big Bang at minus infinity.

To talk about "events before the Big Bang" takes us into an imaginary universe, which by perfect linguistic synchronicity happens to be precisely the realm of religion. :)

They have to. The equations for electronic circuits are full of imaginary numbers. They use hyperbolic trigonometry and all that stuff. Electrical engineering really blurs the boundary between math and physics. In my dad's day electrical engineers used j as the symbol for -1^.5 . I think the standardization on i to conform to the usage of other disciplines occurred in the 1950s. By the time I started studying it in the 1960s it was i.

I wasn't aware it ever got standardized. Every EE I know still uses j, since, in circuits, i typically refers to current...