(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that when f(z)=x^3+i(1-y)^3, it is legitimate to write:

f'(z)=u_x+iv_x=3x^2

only when z=i

2. Relevant equations

Cauchy riemann equations:

u_x=v_y , u_y=-v_x

f'(z)=u_x+i*v_y

3. The attempt at a solution

u=x^3

v=(1-y)^3

u_x=3*x^2

v_y=-3*(1-y)^2

x^2=-(1-y)^2 =

u_y=0

-v_x=0

f'(z)=3*x^2+i(0)= 3*x^2

I don't understand why z=i => z=o+i*1? is relevant to show that f'(z)=3*x^2

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# Homework Help: Cauchy Riemann Problem

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