- #1

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## Homework Statement

z→x

^{3}+ i(1 - y)

^{3}: Show where the functions is analytic and differentiable.

## Homework Equations

## The Attempt at a Solution

For a function to be analytic cauchy-riemann equations must hold.. so

u

_{x}= v

_{y}and u

_{y}= -v

_{x}

Now f(z) = x

^{3}+ i(1 - y)

^{3}is already in the form u(x,y) + iv(x,y) with u(x,y) = x

^{3}and v(x,y) = (1 - y)

^{3}So:

u

_{x}= 3x

^{2}; v

_{y}= -3(1 - y)

^{2}and

u

_{y}= 0 ; -v

_{x}= 0

Does this then mean cauchy-riemann does not hold anywhere but 0 so f is not differentiable on a neighbourhood of any point in

**C**which means it is nowhere analytic.