Grade 11Algebra

find the value of iota raise to the power iota

prabhjyot singh

14 Years agoGrade 11

4 Answers

Aman Bansal

14 Years ago

Dear Prabhjyot,

cos@ + i.sin@ = e^(i.@)
if we take @ = pi/2:
i = e^(i.pi*/2)
Raise both sides to exponent i:
i^i = e^ (i.pi/2 . i)
i^i = e^(-pi/2)

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Aman Bansal

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Priyansh Jain

9 Years ago

Answer of i^i is not e^i(-π/2) because its argument as given in my book is 0. But the answer e^i(-π/2) is a contradiction.

Umar

6 Years ago

The domain of exponential function is all real numbers.....and real numbers are the subset of complex numbers which means we cannot give ì(iota) as power.......iota is an imaginary quantity so how can we prove of something like imaginary raise to power imaginary...