Plotting Functions with Imaginary Terms: Calculator Guide

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Homework Statement



How do I plot a function with an imaginary term (e.g. a*exp (ix), etc.)? More importantly, how would I do it on a calculator.

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The Attempt at a Solution

 
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You don't - unless you do it in 3 dimensions using, say, the y- axis for the real part of the function value and the z- axis for the imaginary part of the function value. That, of course, assumes that the independent variable, x, is a real number since there is only one dimension left for it.
 
I see. I am a bit confused, since I have a problem asking me to plot a function with an imaginary term. Perhaps I have done it wrong (though I have looked over it and can't find an error) or I must plot in three dimensions.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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