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# Complex Numbers

"Complex" numbers share many properties with the real numbers. In fact, complex numbers include all the real numbers, so you know lots of them already. Such an overachiever.

**Details:** \( \bar{z}=x-iy\) and \(i=\sqrt{-1}\).

How many complex numbers are the conjugate of their own cube?

Find the only possible integer value of \(p+q\).

\[\large e ^{ i\theta }e^{ 2i\theta} e^{ 3i\theta }...\large e^{ ni\theta } = 1\]

Find the value of \(\theta\) satisfying the above equation for \(m\in\mathbb{N}\).

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