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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
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.
Where are you coming from with the absolute value?
x need not be positive. The function is odd. You are correct.
thank you zach
that is the confirmation i needed.
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
Yes. :)Quote:
Originally Posted by xviddivxoggmp3
Nice division by 0, major_small. :cool: :D
your negative slipped back into the brackets after all that work to pull it out!Code:=(-1)(x)^3 + x // since f(x) != f(-x) then not even
=(-x)^3 + x
try..
Code:=(-1)(x)^3 + x // since f(x) != f(-x) then not even
=-(x)^3 + x
yeah, it's fun watching people try to figure that out ;)Quote:
Originally Posted by Zach L.
somebody gave me negative rep for that because it was "irrelevant"... I thought that
was the end of the thread...Quote:
Originally Posted by xviddivxoggmp3
How about this one:Quote:
Originally Posted by major_small
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
The step of taking logs of points in the complex plane and getting pure imaginaries seems a bit sketchy.
If exp(number1) = exp(number2), aren't those two numbers the same? :)
:)
it looks more like the beginning of the thread.
;0)
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.
is this valid?Quote:
exp( -pi*i ) = exp( pi*i ) //Eulers formula
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?
Nothing to do with C++Quote:
Originally Posted by xviddivxoggmp3
exp(x) = e^x = 2.71828...^x
And yes, that step is valid, but the next step is illegal, the correct step would be something like:
-pi = pi + 2*n*pi
It depends on how you define logarithm. I could define ln for a complex number z to be:Quote:
Originally Posted by Zach L.
ln z = ln|z| + i*arg(z) , (0<=arg(z)<=2*pi)
Then e^ln(z) = z for all complex numbers z
I guess that could be one definition.
EDIT:
http://www.efg2.com/Lab/Mathematics/...sAndPowers.htm
Nifty... Makes sense. :)