This is Real.pic.twitter.com/E5JQYz39dp
Show this thread
-
-
Note though, when taking powers of complex numbers we have to be careful. Technically, if we don't restrict the range of θ to be [0,2π) then i^i takes on infinitely many values. All of which, however, are real.
Show this thread -
Proof that 𝑖ⁱ is real and equal to exp(-π/2). (Note: we are working in the principal branch of eⁱˣ)pic.twitter.com/OUo4TSJCDk
Show this thread
End of conversation
New conversation -
-
-
Hmmmm
Not quite sure about that radical being used with imaginaries 
-
I agree.
- 10 more replies
New conversation -
-
-
Is it true?
-
yup! in the principal branch!
End of conversation
New conversation -
-
-
obviously
@elonmusk needs to follow me, then - 18 more replies
-
-
-
z=cos 90 +i sin 90 =i, so theta is 90 Now, writing in z=r e ^ i {theta} form, z=e ^i(pie/2) {r=1 since sin^90+cos ^90=1} Now, i ^ (1/i)= e ^{i(pie/2)}*1/i =e^(pie/2), hence proved
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
Ah, brings back memories. Caught the attention of a math prof in the first class meeting by answering this one in a couple seconds while everyone else in class looked at me like I'd grown an extra head.
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.