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How can we write the complex number 2 in polar form?

$r =\sqrt(2^2) = 2$

$z =2(\cos 0 + i \sin 0)$

The question is, do we use $\theta = 0$ or $\theta = 2 \pi$

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  • $\begingroup$ its polar form is $2$ because imaginary part is zero. $\endgroup$ – R.N Sep 18 '15 at 0:50
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All answers of the form $$2(\cos 2k\pi +i\sin 2k\pi)$$ are correct.

However, one typically has in mind a specific half-open interval of length $2\pi$ in which the polar angle $\theta$ should lie. For example, one may require $\theta\in(-\pi,\pi]$, or $\theta\in [0,2\pi)$, or $\theta\in (0,2\pi]$, etc., so the answer that is sought will depend on the interval required (which you have not specified).

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They're equivalent of course, but your teacher probably wants the simplest form, theta = 0.

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