What are complex derivatives?

Complex derivatives are descriptions of the degree of changes in complex functions that work in value fields that include imaginary numbers. They tell mathematics about the behavior of functions that are difficult to visualize. The comprehensive function of f v x _{0 , if exists, is given by the limit because X is approaching x Another field, which is an event called mapping. When one or both of these fields contains numbers that are part of the field of complex numbers, the function is called a complex function. Complex derivatives come from complex functions, but not every complex function has a complex derivative. These are values ​​that can be represented by A + B I , where A and B are real numbers A i is the role of negative, which is an imaginary number. Value B can be zero, so all real numbers are also complex numbers.}

DeriVata is the measure of changes in functions. In general, a derivative is a measure of units of change above one axis for each unit of a different axis. For example, a horizontal line on a two -dimensional chart should be a derivative of zero, because for each X unit, the value of Y changes by zero. The immediate derivatives that are most commonly used provide the speed of change at one point on the curve rather than through the range. This derivative is the slope of the line that is tangible to the curve at the desired point.

However, there is no derivative everywhere for every function. For example, if the function has a corner in it, there is no derivative in the corner. This is because the derivative is defined by the limit, and the derivative makes a jump from one to another, then the limit does not exist. The function that has derivatives is said to be differentiated. One condition for differentiability in complex functions is that partial derivatives or derivatives for each axis must be continuous at a given point.

Complex functions that have complex derivatives must also meet the conditions called Cauchy-Riema functionsnn. They require complex derivatives to be the same regardless of how the function is oriented. If the conditions set by the functions are met and partial derivatives are continuous, the function is complex differential.