Imaginary numbers

[Freeman]

OK, I know a few, like 'i', but I don't know 'e'. Can someone explain it to me> And tell me if there are any other imaginary numbers?

[jordan]

e isn't imaginary.

 

There are an infinite number more imaginary numbers (though they can all be expressed in terms of "i" if that's what you mean)

 

Like:

 

sqr(-10)

sqr(-43)

Basicly, the square root of any negative number is imaginary.

[Freeman]

Oh... I see. What is e?

[bloodhound]

e is just another real constant. its irrational and transcendental.

 

it can be written as a series. sum from n=0 to inf of 1/n!

 

also can be written as a limit

 

e= lim (n tends to inf) (1+1/n)^n

 

and lim (n tends to inf) (1+1/n)^(n+1)

 

the graph below shows the two functions above and the constant value of e

 

[bloodhound]

also the exponential function of e . i.e e^x has the special property that its gradient at a point is equal to the value of the function at that point. dont know if there are other functions with this property

[JaKiri]

it can be written as a series. sum from n=0 to inf of 1/n!

 

This is acquired from putting the property 'when differentiated, it remains the same' into a maclaurin series.

 

It's pretty clear, from this method, that there are no similar numbers.

[bloodhound]

i am quite unsure. was e discovered first as constant and then e^x being the same as diff e^x

 

or was that condition forced to caculate the value of e

[Dave]

I think that was the condition, although I could be (and probably am) wrong.