Functions in Two-Dimensional Vector Space or Complex Plane
Functions in Two-Dimensional Vector Space or Complex Plane
This Demonstration illustrates that functions in a real two-dimensional vector space are equivalent to functions in the field of complex numbers. Specifically, we consider a class of functions of the form , where and are different integers. The black arrow traces out the function , shown as a black curve, while the two component vectors are represented by red and blue arrows, tracing out red and blue circles.
Z(z)=a+b
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Z(z)