Is it possible for me to model mathematically the revolution to sharpen a pencil using complex number?

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I was planning to do research on complex number since I find the topic intriguing, How can I conduct a research by modelling mathematically to calculate the required number of rotation for a pencil in a circular motion when sharpening the pencil with a sharpener using complex number by linking the number of rotations, length of graphite and the time taken?