Find regular function. Complex analysis.

[Солунац]

Привет!

One problem from complex analysis that I couldn't solve. Please help.
(a) Find regular function $g(z) = u(x, y)+iv(x, y)$ if $u$ has a shape of $u(x, y) = f(\frac{x^2+y^2} y)$, where $f$ is real function of real variable.
(b) Show that function $g(z)$ could be represented in the shape of $g(z) = \frac{c_1} z + c_2$, where $c_1$ and $c_2$ are complex constants.

Спасибо.

[Taras]

it can be easily solved using Cauchy-Riemann equations.

[Gafield]

The function $h(x,y)=\frac y{x^2+y^2}$ is harmonic. So from

$$ \Delta f(h)=|\nabla h|^2f''(h)=0$$

we have $f''=0$.

[Danila88]

Use a conditions of Khoshi-Riman

[Хорхе]

Danila88 писал(а):

Use a conditions of Khoshi-Riman

This (Indian?) mathematician I don't know. I failed to find him in Google

[ewert]

Не удивительно, ибо он эмигрировал в Индию сперва из Франции, а потом из Германии. До эмиграции же его звали Cauchy-Riemann.