rizardon said:Why don't you try and do the partial fraction. I think it should work.
Complex analysis is a branch of mathematics that studies functions of complex variables. It deals with the properties and behavior of functions that have complex inputs and outputs, and how these functions can be manipulated and analyzed.
This function is a rational function that takes a complex number z as an input and outputs another complex number. It is a specific example of a rational function, which is a function that can be written as the ratio of two polynomial functions. In this case, the numerator is z+i and the denominator is z^2+1.
To express a function in terms of real and imaginary parts, we use the Euler's formula, e^(ix) = cos(x) + i*sin(x). By substituting e^(ix) for z in the function f(z), we can rewrite it as w = (e^(ix)+i)/(e^(2ix)+1). Then, we can expand the numerator and denominator using the binomial theorem and simplify to get the real and imaginary parts of w in terms of x and y.
To find the real and imaginary parts of this function, we can use the method mentioned in the previous question. After expanding and simplifying, we get u(x,y) = (x-y)/(x^2+y^2+1) and v(x,y) = (x+y)/(x^2+y^2+1). These are the real and imaginary parts of the function w = u(x,y)+iv(x,y).
To plot this function, we can use the real and imaginary parts we found in the previous question. We can plot points on the complex plane using the values of x and y, and connect them to create a graph. This graph will show the behavior of the function as it takes different complex values as inputs.