If a complex function can be integrated,can we get the function back?
2006-09-16 04:17:47 · 5 answers · asked by Kenneth Koh 5 in Science & Mathematics ➔ Mathematics
Yes, indeed. For example,
sin(x) = (e^(ix) + e^(-ix))/2
is a complex function that you integrate all the time without giving it a second thought!
Good Luck.
2006-09-16 04:50:55 · answer #1 · answered by alrivera_1 4 · 1⤊ 0⤋
Yes, they can. For example, instead of f(x)=x^2 consider f(z)=z^2, where z is a complex variable. The derivative is still 2z and the integral is still z^3/3. All functions don't have such an easy complex analogue however.
2006-09-16 11:48:32 · answer #2 · answered by bruinfan 7 · 1⤊ 0⤋
Calculus and elementary functions
If the argument is complex, the expression will be rewritten using the Ln function. ... in the list expr is differentiated...
yacas.sourceforge.net/refchapter5.html
Complex Variables
Such series can always be differentiated and integrated term by term, a property ... his rigorous theory of complex...
www.du.edu/~jcalvert/math/complex.htm
Complex Analysis
... real differentiable functions even of many variables (the complex numbers are ... It can be shown that this integral...
www.physicsforums.com/showthread.php?t...
2006-09-16 11:22:47 · answer #3 · answered by Anonymous · 0⤊ 1⤋
Yes. it is advanced level in math.
2006-09-16 11:22:01 · answer #4 · answered by iyiogrenci 6 · 0⤊ 1⤋
yes
2006-09-16 11:19:07 · answer #5 · answered by atheistforthebirthofjesus 6 · 0⤊ 1⤋