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Is it true that a function is analytic iff it satisfies the Cauchy-Riemann equations? I am reading Freitag's Complex Analysis and I am asked to show that ${\partial f\over \partial \bar{z}}=0$ iff $f$ is analytic. Is this because $f$ is analytic iff it satisfies the CR equations iff ${\partial f\over \partial \bar{z}}=0$? (It is obvious that $f$ satisfies CR $\implies {\partial f\over \partial \bar{z}}=0$ but what about the other relations? Are they true? I know that if a function is analytic, it must satisfy CR equations, but I don't know if the other direction is true or if ${\partial f\over \partial \bar{z}}=0$ necessarily mean that CR equations are satisfied.)

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