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## Homework Statement

show that the function f(z)=zRe(z) is only differentiable at the origin.

im completely lost with is, its probably very easy.. but dont know how to start.

f(x+iy)=x+iy*Re(z)=x(x+iy)??? idk

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- Thread starter fredrick08
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show that the function f(z)=zRe(z) is only differentiable at the origin.

im completely lost with is, its probably very easy.. but dont know how to start.

f(x+iy)=x+iy*Re(z)=x(x+iy)??? idk

- #2

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u is the real part of the function and v is the imaginary part, and u_x is the derivative of u with respect to x etc.

As you stated, the function can be written as x(x+iy) = x^2 + ixy, so u = x^2, v = xy. You will find the functions only satisfy the C-R equations at the origin.

- #3

gabbagabbahey

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im completely lost with is, its probably very easy.. but dont know how to start.

f(x+iy)=x+iy*Re(z)=x(x+iy)???

So far so good, now what are the real and imaginary parts, [itex]u(x,y)[/itex] and [itex]v(x,y)[/itex], of this expression? What conditions must the partial derivatives of [itex]u(x,y)[/itex] and [itex]v(x,y)[/itex] satisfy for f(x+iy) to be differentiable?

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