Cauchy-Riemann

Let f(z) be an analytic function, where z = x + iy. If the real part of f(z) is cosh x cos y, and the imaginary part of f(z) is zero for y = 0, then f(z) is

Let f(z) be an analytic function, where z = x + iy . If the real part of f(z) is cosh x cos y , and the imaginary part of f(z) is zero for y = 0 , then f(z) is

An analytic function $f(z)$ of complex variable $z=x+iy$ may be written as $f(z)=u(x, y)+iv(x, y)$. Then, $u(x, y)$ and $v(x, y)$ must satisfy

$F(z)$ is a function of the complex variable $z = x+iy$ given by $F(z) = i z + k Re(z) + i Im(z)$. For what value of $k$ will $F(z)$ satisfy the Cauchy-Riemann equations?

An analytic function of a complex variable $$z=x+iy,$$ where $$i = \sqrt { - 1} $$ is expressed as $$f\left( z \right) = u\left( {x,y} \right) + i\,v\left( {x,y} \right).\,$$ If $$...

If $$\phi (x,y)$$ and $$\psi (x,y)$$ are function with continuous 2 nd derivatives then $$\phi (x,y)\, + \,i\psi (x,y)$$ can be expressed as an analytic function of x +iy ($$i = \s...