- #1

inversquare

- 17

- 0

[tex]z\in\mathbb C[/tex]

I imagine it is not too difficult, I'm just missing something. I need to use the limit definition to prove it,

[tex] lim_{Δz\rightarrow 0} \frac{f(z+Δz)-f(z)}{Δz} [/tex]

Alternatively, using Cauchy-Riemann conditions, am I correct to assume

[tex]u(x,y) = x^2 + y^2[/tex] and [tex] v(x,y) = 0 [/tex]

Then,

[tex]u_x ≠ v_y[/tex] and [tex]u_y ≠ - v_x[/tex]

?

Thanks!

Chad

I imagine it is not too difficult, I'm just missing something. I need to use the limit definition to prove it,

[tex] lim_{Δz\rightarrow 0} \frac{f(z+Δz)-f(z)}{Δz} [/tex]

Alternatively, using Cauchy-Riemann conditions, am I correct to assume

[tex]u(x,y) = x^2 + y^2[/tex] and [tex] v(x,y) = 0 [/tex]

Then,

[tex]u_x ≠ v_y[/tex] and [tex]u_y ≠ - v_x[/tex]

?

Thanks!

Chad

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