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6 Pages Essays / Projects Year Uploaded: 2022

The investigation explored the transformation of complex numbers on the argand plane when raised to a power n. The investigation first explored the relationship between certain values z^n and developed a conjecture allowing for the prediction of certain z^n where n is a large number. The investigation further explored complex numbers by introducing a complex number a+bi equal to z. This new complex number was raised to the power n and it, too, was calculated and displayed on an argand diagram to explore the transformation. In addition to this, the relationship between z^n and its modulus and argument were also explored to develop a conjecture replicating De Moivre’s theorem. This theorem was also proven utilizing the principal of mathematical induction to ensure the conjecture holds true for all values of n. Assumed knowledge of the value of i, the method for calculating a complex number’s modulus and argument, and consequently its polar form, and Argand plane is used.


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