This question to help beginners to distinguish between analysis in real line and complex plane. So:
Give only a characteristic difference between dealing with a function in "real analysis" and "complex analysis"? for example, domain, range, graph representation, limits, continuity, ... etc.
Let us consider the derivative of a function.The definition is same, for example f'(x)=f(x+h)-f(x)/h
In Real analysis, h approaches zero either from right limit or left limit. But, in complex analysis, h->0 means, it can take infinite number of paths to approach zero. Also, it can spiral in.
Also a function differentiable in real need not be differentiable in complex
Also, differentiation in complex is strong than real one.
If a function is differentiable in real, it need not be true that it has all derivatives.
But, it is true in complex. That is, existence of one derivative implies the existence of all derivatives.
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