Challenge Question: What is i^i, where i = sqrt(1)

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

Challenge Question: What is i^i, where i = sqrt(1)

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

But... \(\sf i = \sqrt{-1}\)
|dw:1434833839810:dw|
maybe its better to rewrite in polar form

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Yep! $$ \Large{ i^i=\sqrt{-1}^{\sqrt{-1}}=? } $$
|dw:1434833909276:dw|
feels like i cheated just using euler form hehe
That's it! Fantastic that an imaginary numbers like that make a real number!
yes pretty cool
however -.- i dont think imaginary numbers are any different form real numbers
the term "imaginary" is needlessly misleading
@ybarrap what is your interpretation of a number raised to the power of an imaginary number though
I'm with you, I think Euler -- I think rotations and this particular rotation keeps us on the real axis $$ e^{nix}=(\cos x + i \sin x)^n\\ {e^{\pi i/2}}^i\text{ (i.e. a rotation)}=(\cos \pi/2 + i \sin \pi/2)^i=\text{ a real number}\\ $$
mhm its just a bit weird to think about, i was just thinking, okay building up exponent laws for integers, fractions, then negative numbers get a bit weird, and imaginary numbers cant wrap my head around it

Not the answer you are looking for?

Search for more explanations.

Ask your own question