Do you mean, "Does z go from 0 to ∞?" Your question is unclear, which is why no one will answer.CrimsonFlash said:Homework Statement
It is simply the same as the one for lnz i.e. does it go from 0 to ∞?
Also, is there any proper way to figure out branch points of a function?
A branch cut for (lnz)^2 is a mathematical concept used in complex analysis to define the multi-valued function lnz. It is a line or curve on the complex plane where the function is discontinuous and needs to be "cut" in order to make it single-valued.
A branch cut is necessary for (lnz)^2 because lnz is a multi-valued function, meaning it can have multiple values for a single input. This can cause issues in mathematical calculations, so a branch cut is used to define a specific range of values for lnz and make it single-valued.
The branch cut for (lnz)^2 is typically chosen along the negative real axis, starting at the origin and extending to negative infinity. This is known as the principal branch cut and is the most commonly used branch cut for lnz.
A branch cut and a branch point are closely related concepts. A branch point is a point on the complex plane where a function becomes multi-valued, while a branch cut is the line or curve used to make the function single-valued. Branch points are often located at the endpoints of branch cuts.
The branch cut for (lnz)^2 affects the values of the function by restricting them to a specific range. For example, the principal branch cut for lnz allows the function to have values between 0 and 2π, while other branch cuts may have different ranges. This ensures that the function remains single-valued and avoids any mathematical inconsistencies.