anonymous
  • anonymous
Find the holomorphic function f(x+iy) such that Re f(x+iy)= cosh(3y)sin(3x) and f(0)=0
Mathematics
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
ugh i havent taken calc yet so i cant do this
anonymous
  • anonymous
cauchy reimann yes?
anonymous
  • anonymous
yes satellite

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
so the derivative of this wrt x must be the derivative of the imaginary part wrt y right? the derivative is \[3\cos(3x)\cosh(3y)\] integrate wrt y and get \[\cos(3x)\sinh(3y)\] i think.
anonymous
  • anonymous
it's been a while. am i on the right track?
anonymous
  • anonymous
you also need the partial wrt y is minus the partial wrt x of the imaginary part. if we are lucky it already is oh and you also need that f(0)=0 i forgot the +C when i integrated
anonymous
  • anonymous
how to you like that? i miracle! it works
anonymous
  • anonymous
so i guess unless i totally screwed this up the answer is \[f(x+iy)=\cosh(3y)\sin(3x)+\cos(3x)\sinh(3y)\]
anonymous
  • anonymous
think we lost raheen maybe he will be back
anonymous
  • anonymous
rather \[f(x+iy)=\cosh(3y)\sin(3x)+i\cos(3x)\sinh(3y)\]
anonymous
  • anonymous
i forgot the i part
anonymous
  • anonymous
@raheen look ok?
anonymous
  • anonymous
it does not come with a money guarantee because it has been several years but i think it looks good. you can check cauchy reimann equations for this and see if they work
anonymous
  • anonymous
satellite you are about to reach , great work I think you did how about using the 2 conditions of C-R then you need to integrate and don forget to find the constant
anonymous
  • anonymous
well i integrated wrt y and got the answer. then i checked that the second equation and it worked. and by inspection you can see that \[f(0)=0\]
anonymous
  • anonymous
i mean if the C-R equations are going to work, then after i take the derivative wrt x and integrate wrt y , then the second condition \[\frac{\delta u}{\delta y}=-\frac{\delta v}{\delta x}\] had better work or else we are screwed. both conditions must hold. but in any case i checked and they do
anonymous
  • anonymous
that's so great satellite, thank you.
anonymous
  • anonymous
yw
Zarkon
  • Zarkon
the only thing I would add is that when you integrated with respect to y you don't get C you get some function of x
anonymous
  • anonymous
Zarkon, thank you, you are right it's C(x)
Zarkon
  • Zarkon
It doesn't look like it will change the final answer though

Looking for something else?

Not the answer you are looking for? Search for more explanations.