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# Imaginary number in a graph

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So can a imaginary number be in a graph like:$$\frac{\sqrt-1}{\sqrt-3}$$ Since the i can cancel out

Jul 26, 2022

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$$\frac{i\sqrt{1}}{i\sqrt{3}}=\frac{1}{\sqrt{3}}$$ which is a real number.

So, this number can be represented on a real number line. (No need for complex plane (argand diagram).)

Yes, we first "simplify" the number then we put it.

And the number is not imaginary; it is real.

Jul 26, 2022
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That's very interesting! I know another strange fact that i^i is even real!

i = e^{pi/2i}

$$e^{\pi i/2 \cdot e^{\pi i/2}}$$ = $$e^{\pi i^2 /2 }$$

The i^2 cancels out as negative and we see that $$e^{-\pi/2}$$ = i ^i which is actually real!

Cool, isn't it! :)

Jul 26, 2022