Hi ppl, would love the solutuin to "show that f(Z) = Z(hat) is not differentiable"

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- March 24th 2011, 11:23 AMdavy337Show that f(Z) = Z(hat) is not differentiable.
Hi ppl, would love the solutuin to "show that f(Z) = Z(hat) is not differentiable"

- March 24th 2011, 11:31 AMFernandoRevilla
- March 24th 2011, 08:49 PMmr fantastic
- March 25th 2011, 05:08 AMHallsofIvy
Or you could use the reasoning that leads to the Cauchy-Riemann equations. Let z= x+ iy where x and y are real numbers. Then . To find the derivate at, say we form the "difference quotient" and take the limit as z goes . Since that is a two dimensional limit, in order that the derivative exist, the limit must be the same as we approach from any direction.

In particular, what do we get if we approach along the line ?

What do we get if we approach along the line ? Are those the same? - March 25th 2011, 02:28 PMmr fantastic