# Mathematics Odd/Even Functions

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• 10-16-2004
xddxogm3
Mathematics Odd/Even Functions
My mathematics book is very poor on it's explinations, so can someone look at my logic and tell me if I understand this correctly. I'm looking for a yes or no.
Code:

```  f(x)=x^3 - x     f(-x)=(-x)^3 - (-x)           =(-1)^3 (x)^3 + x           =(-1)(x)^3 + x // since f(x) != f(-x) then not even           =(-x)^3 + x           =(-1)(x^3 - x) //odd           =-f(x)   f(-x) = -f(x) Odd```
• 10-16-2004
abyssphobia
hey you are taking algebra math mmm me too !!! Im seeing the same thing :)
yes, you are right
But in this part, I'm not quite sure
Quote:

=(-1)(x^3 - x) //odd

=-f(x)

f(-x) = -f(x) Odd

ok but X has to be positive (absolute value |x| )
because of the result. I guess, still unsure.
• 10-16-2004
Zach L.
Where are you coming from with the absolute value?

x need not be positive. The function is odd. You are correct.
• 10-16-2004
xddxogm3
thank you zach
that is the confirmation i needed.
• 10-17-2004
major_small
Code:

```        X = Y X^2 - Y^2 = XY - Y^2 (X+Y)(X-Y)=Y(X-Y) (X+Y)(X-Y) = Y(X-Y)   (X-Y)      (X-Y)       (X+Y)=Y     If X=1 and Y=1       (1+1)=1```
• 10-17-2004
Sang-drax
Quote:

Originally Posted by xviddivxoggmp3
I'm looking for a yes or no.

Yes. :)
• 10-17-2004
Zach L.
Nice division by 0, major_small. :cool: :D
• 10-17-2004
Perspective
Code:

```=(-1)(x)^3 + x // since f(x) != f(-x) then not even   =(-x)^3 + x```
your negative slipped back into the brackets after all that work to pull it out!
try..
Code:

```=(-1)(x)^3 + x // since f(x) != f(-x) then not even   =-(x)^3 + x```
• 10-18-2004
major_small
Quote:

Originally Posted by Zach L.
Nice division by 0, major_small. :cool: :D

yeah, it's fun watching people try to figure that out ;)

somebody gave me negative rep for that because it was "irrelevant"... I thought that

Quote:

Originally Posted by xviddivxoggmp3
thank you zach
that is the confirmation i needed.

was the end of the thread...
• 10-18-2004
Sang-drax
Quote:

Originally Posted by major_small
yeah, it's fun watching people try to figure that out ;)

Code:

```cos(-pi) + i*sin(-pi) = cos(pi) + i*sin(pi) //Both equal -1 exp( -pi*i ) = exp( pi*i )  //Eulers formula -pi*i =  pi*i -pi = pi -1 = 1```
• 10-18-2004
Zach L.
The step of taking logs of points in the complex plane and getting pure imaginaries seems a bit sketchy.
• 10-18-2004
Sang-drax
If exp(number1) = exp(number2), aren't those two numbers the same? :)
:)
• 10-18-2004
xddxogm3
it looks more like the beginning of the thread.
;0)
• 10-18-2004
Zach L.
Right... What I was getting at is that the complex plane can be viewed as a field in its own right, or a vector space over R. I'm not sure if log is suitably defined over the field, and I am rather sure that it is not defined over C as a vector space.
• 10-18-2004
xddxogm3
Quote:

exp( -pi*i ) = exp( pi*i ) //Eulers formula
is this valid?
I have very little experience with complex numbers in C++.
Isn't there a complex number class or variable object?
Is exp() a function that accepts complex numbers?
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