Show that when f(z)=x^3+i(1-y)^3, it is legitimate to write f'(z)=ux+ivx=3x^2 only when z=i.
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Originally Posted by bethh Show that when f(z)=x^3+i(1-y)^3, it is legitimate to write f'(z)=ux+ivx=3x^2 only when z=i. The question you should be asking is when is analytic then the formula is valid. So check the cauchy-reimann equations and Now for what points (x,y) does this gives The only solution to this equation is (0,1) this is the same as the complex number also note that
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