The Simple Theorem of Numbers

The Simple Theorem of Numbers

This is a simple proof that each real number undergoing a normal operation is equal to a real number.

$$\sqrt{-1} = \sqrt{-(1)} = \sqrt{-(\sqrt{1})^{2}}$$

Since,

$$\sqrt{x^{y}} = \sqrt{x}^{y}$$

Then,

$$\sqrt{-(\sqrt{1})^{2}} = \sqrt{-(\sqrt{1})}^{2}$$

Thus,

$$\sqrt{-1} = -\sqrt{1} = -1$$

Or generally,

$$\sqrt{-n} = -\sqrt{n}$$
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