analytic function

Which one of the following functions is analytic over the entire complex plane?

Consider the complex valued function $$f\left( z \right) = 2{z^3} + b{\left| z \right|^3}$$ where $$z$$ is a complex variable. The value of $$b$$ for which the function $$f(z)$$ is...

Let $$z=x+iy$$ be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction . Which one of the following statement is NOT...

The real part of an analytic function $$f(z)$$ where $$z=x+jy$$ is given by $${e^{ - y}}\cos \left( x \right).$$ The imaginary part of $$f(z)$$ is