MHB Can you please tell me if this question is Correct?

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"Show that u(x,y) = e3x((3y-2)cos(3y)-2xsin(3y)) is holomorphic in C.

Hence Find the complex Potential f(z) such that u(x,y)=Re(f(x+iy))."

Well i think it should be harmonic because we cannot show that Re(z) is holomorphic and hence find its Complex Potential, just want you to confirm that with me.
 
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shen07 said:
"Show that u(x,y) = e3x((3y-2)cos(3y)-2xsin(3y)) is holomorphic in C.

Hence Find the complex Potential f(z) such that u(x,y)=Re(f(x+iy))."

Well i think it should be harmonic because we cannot show that Re(z) is holomorphic and hence find its Complex Potential, just want you to confirm that with me.
I agree with you. A real-valued function cannot be holomorphic (unless it is constant). The question should be asking whether u(x,y) is harmonic, not holomorphic.
 
Opalg said:
I agree with you. A real-valued function cannot be holomorphic (unless it is constant). The question should be asking whether u(x,y) is harmonic, not holomorphic.
Ok. Thanks..But the function also is not right then? because LaPlace's Equation does not hold from that function..
 
shen07 said:
"Show that u(x,y) = e3x((3y-2)cos(3y)-2xsin(3y)) is holomorphic in C.

Hence Find the complex Potential f(z) such that u(x,y)=Re(f(x+iy))."

Well i think it should be harmonic because we cannot show that Re(z) is holomorphic and hence find its Complex Potential, just want you to confirm that with me.

shen07 said:
Ok. Thanks..But the function also is not right then? because LaPlace's Equation does not hold from that function..
You're right again! As it stands, that function is not harmonic. Perhaps the last 2 is a misprint for a 3. Then $u(x,y) = e^{3x}\bigl((3y-2)\cos(3y)-\mathbf{3}x\sin(3y)\bigr)$ is harmonic, being the real part of $-(3iz+2)e^{3z}.$
 
Opalg said:
You're right again! As it stands, that function is not harmonic. Perhaps the last 2 is a misprint for a 3. Then $u(x,y) = e^{3x}\bigl((3y-2)\cos(3y)-\mathbf{3}x\sin(3y)\bigr)$ is harmonic, being the real part of $-(3iz+2)e^{3z}.$

Hey Thanks a lot for that, i would have passed hours to find that error, I am really greatful to you.
 
I posted this question on math-stackexchange but apparently I asked something stupid and I was downvoted. I still don't have an answer to my question so I hope someone in here can help me or at least explain me why I am asking something stupid. I started studying Complex Analysis and came upon the following theorem which is a direct consequence of the Cauchy-Goursat theorem: Let ##f:D\to\mathbb{C}## be an anlytic function over a simply connected region ##D##. If ##a## and ##z## are part of...
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