Interesting question: why is ln(-1) in polar form....?

[rabualeez]

Hi all,
I was doing some math and I stumbled upon a very interesting thing. When I do ln(-1), I get πi, and when I turn that into polar coordinates on the calculator, it gives me πe^iπ/2 . Why is that? I'm very curious to know, because they are so intertwined!

Thank you

 

[BvU]

Hello Rabu,

Apparently, $i$ and $e^{i\pi/2}$ are one and the same. Can you see why ?
The calculator responds in a form $|\alpha| \,e^{\operatorname{\, Arg}(\alpha)}$ which I think is reasonable for complex numbers.