Microsoft COM for Complex Variables

Short Description
Our senior mathematics course in Complex Variables uses technology for complex arithmetic and mappings. Microsoft COM technology is used to produce a component in Visual Basic code that can be used in programs or in Excel. The component encapsulates the data structure and operations for complex arithmetic. The component is used in programming projects for complex valued computations and plotting. We show example projects and how to create the COM complex component.

Website: archives.math.utk.edu | Filesize: 87kb
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Content
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Complex numbers are composed of two real quantities. Arithmetical operations on such manipulate the two and produce results using real arithmetic. We usually program this one quantity at a time. However in a course focused on Complex Variables this is unproductive work for the participants. We create for them a component that allows reference to a complex number and its arithmetic by normal programming constructions. The technology that allows us to do this with ease is the Microsoft COM technology for encapsulating a data structure and its operations in a programming unit that can be referenced in a program. The component is connected to an Excel spreadsheet using Visual Basic Application (VBA is the macro language built into Excel) to compute the complex values. The class project included: the computation of parallel impedance’s, plotting the complex valued output of a bandpass filter, using complex valued functions to estimate the real derivative of a function, to make a 3d plot of the magnitude of a complex valued function of a complex variable, and finally to show how a circle in the complex plane is mapped by a complex valued function of a complex variable.
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