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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
 #1
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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
 #2
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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

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