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-1. It is a version of Euler's formula.
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∙ 11y ago
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How do you manually calculate i to the power of i?
i (taken to be sqrt(-1) for this question) requires that you know a bit about writing complex numbers. i = e^(i*pi/2) so i^i = (e^(i*pi/2))^i which equals e^(i*i*pi/2) since i*i = -1 we get e^(-pi/2) so i^i = e^(-pi/2) which is roughly .207879576
Is a power a whole number?
Not necessarily. i times pi is not a whole number, and yet e to the power of i times pi is equal to -1.
What is e to the power of you times pi?
'e' is an imaginary number, multiplied by anything gives an imaginary result
How do you manually calculate i raised to the power of i?
by euler: i=ei(pi)/2 therifore ii = (ei(pi)/2)i=ei^2(pi)/2=e-(pi)/2 ~0.208
What is e plus pi plus pi plus pi plus e plus e plus e?
About 20.29791
How can you make rational of i power i?
It is NOT rational, but it IS real.Start with Euler's formula: e^ix = cos(x) + i*sin(x) for all x.When x = pi/2,e^(i*pi/2) = cos(pi/2) + i*sin(pi/2) = 0 + i*1 = ior i = e^(i*pi/2)Raising both sides to the power i givesi^i = e^[i*(i*pi/2)] = e^[i*i*pi/2]and since i*i = -1,i^i = e^(-pi/2) = 0.20788, approx.
How do you manually calculate i to the power of i?
i (taken to be sqrt(-1) for this question) requires that you know a bit about writing complex numbers. i = e^(i*pi/2) so i^i = (e^(i*pi/2))^i which equals e^(i*i*pi/2) since i*i = -1 we get e^(-pi/2) so i^i = e^(-pi/2) which is roughly .207879576
Is a power a whole number?
Not necessarily. i times pi is not a whole number, and yet e to the power of i times pi is equal to -1.
What is e to the power of you times pi?
'e' is an imaginary number, multiplied by anything gives an imaginary result
Why is it that e to the power of i pi equals -1?
Because Euler proved it! (No, I can't!)
How do you manually calculate i raised to the power of i?
by euler: i=ei(pi)/2 therifore ii = (ei(pi)/2)i=ei^2(pi)/2=e-(pi)/2 ~0.208
What is anything to the power of i?
That really depends what you are raising to the power i.
What is e plus pi plus pi plus pi plus e plus e plus e?
About 20.29791
What is value of iota raise to the power iota raise to the power iota till infinity?
the answer is e raise to power minus pi/2
Is e to the pi rational?
e^pi ~ 23.14069.............., not rational
What is ten raised to the with power?
Using Euler's relation, we know that e^(i*n*pi) = cos(n*pi) + i*sin(n*pi) where n is an integer. We also know that we can rewrite 10 as e raised to a specific power, namely e^(ln(10)). So substituting this back into 10^i and then applying Euler's relation, we obtain 10^i = (e^(ln(10)))^i = (e^(i*ln(10))) = cos(ln(10)) + i*sin(ln(10)).
What is pi to the 5th power?
Pi to the 5th power is approximately 306.019684785
