Mathegoras

Complex numbers › The complex plane › Argument and polar form

Argument of a sum of exponentials

High school · ●●○○○ 20 pts

The number e7πi/60+e17πi/60+e27πi/60+e37πi/60+e47πi/60e^{7\pi i/60} + e^{17\pi i/60} + e^{27\pi i/60} + e^{37\pi i/60} + e^{47\pi i/60} is written in the form reiθre^{i\theta}, where r≥0r \ge 0 and 0≤θ<2π0 \le \theta < 2\pi. Find θ\theta in degrees.

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polar formargument of a complex numberunit circlesymmetry