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# Complex Numbers. Help is appreciated

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Consider the complex number in this picture

We can write

$$z = 2\sqrt{2}e^{i\theta_1} = 2\sqrt{2}e^{i\theta_2} = 2\sqrt{2}e^{i\theta_3}$$
for $$\theta_1, \theta_2, \theta_3$$ between 0 and 6pi. Answer with $$\theta_1, \theta_2, \theta_3$$

Help is really appreciated.

Aug 13, 2022

$$(\theta_1, \theta_2, \theta_3 = \pi/8, 15 \pi/8, 7 \pi/4)$$