find the value of iota raise to the power iota

Aman Bansal
592 Points
10 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)

Best Of luck

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Thanks

Aman Bansal

Priyansh Jain
23 Points
5 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
15 Points
2 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...
Vikas TU
14149 Points
2 years ago
Dear student
i=−1−−−√
i2=(−1−−−√)2=−1
i3=i×i2=i×−1=−i
i4=i2×i2=−1×−1=1
i5=i×i4=i×1=i
i6=i×i5=i×i=i2=−1
i7=i×i6=i×−1=−i
i8=(i2)4=(−1)4=1
i9=i×i8=i×1=i
i10=i×i9=i×i=i2=−1