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    • Thread Starter

    Okay so basically, I know if the cauchy-riemann equations are satisfied everywhere that a complex function is holomorphic. What I was wondering, is if they're not equal everywhere, can you still use the cauchy-riemann equations to find the points at which the function is differentiable or do you have to use first principles? Thanks!

    If it satisfies the CR equations on an open set including z_0, then it's diff at z_0. Satisfying them at the point z_0 is NOT sufficient by itself.
    • Thread Starter

    Okay thank you, that's what I was looking for!
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