{"id":4118,"date":"2020-06-26T19:49:56","date_gmt":"2020-06-26T23:49:56","guid":{"rendered":"http:\/\/faculty.fiu.edu\/~theobald\/?page_id=4118"},"modified":"2022-12-16T17:05:20","modified_gmt":"2022-12-16T21:05:20","slug":"complex_fun","status":"publish","type":"page","link":"https:\/\/faculty.fiu.edu\/~theobald\/fun\/complex_fun\/","title":{"rendered":"complex_fun"},"content":{"rendered":"\t\t
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Data analysis in many fields relies on complex functions, which take and return numbers with both real imaginary parts. Despite wide use, really understanding these functions is tough because, with two dimensional input and two dimensional output there is no obvious way to visualize them. You can still understand complex functions in a purely symbolic way, but below is a tool to explore them graphically. I wrote this when I took complex analysis to help understand the functions we were studying. The input (value of z) and output (value of w) are the fields below, with colors (or arrows) that represent angle (hue) and magnitude (brightness). Choose a function from the list, then place your mouse in the input field, where it’s position specifies the real (left and right) and complex (up and down) value of z. Grid lines are multiples of \u03c0\/2.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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