Question

Q.1 If u = x² - y² + x is a real part of analytic function then find

Corresponding imaginary part

Answer 1

I have u(x,y)=2x2+2x−2y2+1u(x,y)=2x2+2x−2y2+1

To find the analytic function of which uu is a real part, I need to write,

dudx=dvdy⟹dvdy=4x+2⟹v(x,y)=4xy+2y;dudx=dvdy⟹dvdy=4x+2⟹v(x,y)=4xy+2y;

Now, we also need dudy=−dvdx⟹−dvdx=−4y⟹v(x,y)=4xydudy=−dvdx⟹−dvdx=−4y⟹v(x,y)=4xy

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Answer 2

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