Cauchy-Riemann Equations: Proving a Function is Nowhere Differentiable 1

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Using the Cauchy-Riemann Equations to prove that the function f(z) = conjugate(z) is nowhere differentiable. This is a straightforward application of the C.R. equations.

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Omg I can't believe how useful your videos have been to me I search a lot of stuff about complex analysis and I find you in almost all of my searches. Thank you for these videos

kevincardenas

TheMathSorcerer, Great Video. The illustration and proof was perfectly supported by your explanation. Thanks for uploading!

MechanicalEI

nice explanation sir No-where differentiable means not satisfy the CR Equation ....

debasishbiswas

If you're the sorcerer, I'm the sorcerer's apprentice!

astroash

how do you always manage to come to the rescue? love u so dayum much

inthebackwiththerabbish

How to prove that f(z) is differentiable at a particular point or in a particular region or interval

mastrammeena

Well if I may ask and hope you can help me with this question :c
what if I find that, for some complex function, my C-R equations hold if x=0 or y=0 for the first equation and for the second one y=0 or y=2. Does this mean that my function is only diff. at the point (0, 0) and on the line y=2?

kevincardenas

(b) Show that `f(z)=x^(2)y^(2)` is differentiable only at all points of the coordinates axes and hence is analytic nowhere.
.
. please.... Tomorrow is my exam

souravpathania

How to prove f(z) at a particular point is continous

mastrammeena

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