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 \( z_1 z_2 z_3 \cdots z_\infty = i \), 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-by-Step Solution

1. **Express \( z_r \) using Euler's Formula**:
\[ z_r = \cos\left(\frac{\pi}{3^r}\right) + i \sin\left(\frac{\pi}{3^r}\right) = e^{i \frac{\pi}{3^r}} \]
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