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If z = (3)/( 2 + cos theta + I sin thet...

If `z = (3)/( 2 + cos theta + I sin theta)`, then prove that z lies on the circle.

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To prove that \( z = \frac{3}{2 + \cos \theta + i \sin \theta} \) lies on a circle, we will manipulate the expression step by step. ### Step 1: Rewrite \( z \) We start with the expression for \( z \): \[ z = \frac{3}{2 + \cos \theta + i \sin \theta} \] ...
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