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# Why Does the natural logarithm of i equal to i pi /2

## $$ln\left ( i \right ) = i\frac{\pi}{2}$$

To prove the upper identity, we aim to use the Euler's Formula for the complex numbers
$$e^{i \theta} = cos(\theta) + isin(\theta)$$. Since,  $$ln\left ( i \right ) = i\frac{\pi}{2}$$ can be interpreted to $$e^{something} = i$$ and this will prompt us to choose value of $$\theta$$ that serve our need from Euler's Formula. So, by setting the value of $$\theta = \frac{\pi}{2}$$, the right hand side of Euler's formula becomes:

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