If `z_r=cos(pi/(3^r))+isin(pi/(3^r)),r=1,2,3, ,` prove that `z_1z_2z_3 z_oo=idot`

Explanation

To prove that \( z_1 z_2 z_3 \ldots = i \), where \( z_r = \cos\left(\frac{\pi}{3^r}\right) + i \sin\left(\frac{\pi}{3^r}\right) \) for \( r = 1, 2, 3, \ldots \), we can follow these steps:

### Step 1: Express \( z_r \) in exponential form
Using Euler's formula, we can express \( z_r \) as:
\[ z_r = e^{i \frac{\pi}{3^r}} \]

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