Covert the complex number `z = 1 + cos (8pi)/(5) + i. sin (8pi)/(5)` in polar form. Find its modulus and argument.

Explanation

To convert the complex number \( z = 1 + \cos\left(\frac{8\pi}{5}\right) + i \sin\left(\frac{8\pi}{5}\right) \) into polar form, we will follow these steps:

### Step 1: Rewrite the complex number
We start with the given complex number:
\[ z = 1 + \cos\left(\frac{8\pi}{5}\right) + i \sin\left(\frac{8\pi}{5}\right) \]

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