What is the sine of i (initial value prob)

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SUMMARY

The discussion centers on calculating the sine and cosine of the imaginary unit "i" within the context of a second-order differential equation, specifically t²y'' - ty' + y = 0 with initial conditions y(1) = 1 and y'(1) = 1. The user queries whether it is valid to determine the sine of the square root of -1, leading to the conclusion that ω, derived as i from the equation ω² = -(1/t), is indeed correct. The formula for sine, sin(x) = (e^(ix) - e^(-ix))/2, is referenced to find sin(i).

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what is the sine of "i" (initial value prob)

Homework Statement


What is the sine or cosine of i?
does it make sense to ask what sine of root (-1) is?

im asking because its from 2nd order DE: t^2y'' - ty' + y = 0...y(1) = 1 y'(1) = 1


when i rearrranged and determined omega it ended up being i.. is that wrong??

(omega squared = -(1/t) so omega = i)

?

please help...thanks



Homework Equations





The Attempt at a Solution


 
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sinx = (eix - e-ix)/2

so sini = … ?
 


fufufu said:

Homework Statement


What is the sine or cosine of i?
does it make sense to ask what sine of root (-1) is?

im asking because its from 2nd order DE: t^2y'' - ty' + y = 0...y(1) = 1 y'(1) = 1


when i rearrranged and determined omega it ended up being i.. is that wrong??

(omega squared = -(1/t) so omega = i)

You didn't show any work and I don't know what ω is that you are talking about nor what the sine or cosine functions have to do with this problem, let alone the sine of i.
 

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