Easier than it looks

Algebra Level pending

If \(z + \dfrac1z = 2\cos \theta\), and \(z\) is a complex number, \(n\) is a variable, what is the value of \(z^n + \dfrac1{z^n} \)?

A) \( 2ni \sin(n\theta ) \).
B) \( 2i \sin(n\theta ) \).
C) \( 2i \).
D) \( 2 \sin(n\theta ) \).

Clarification: \(i=\sqrt{-1}\).

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