The discussion revolves around the expression y = e^(x(1-i)) + e^(x(1+i)) and its simplification using Euler's identity. Participants are examining the relationship between this expression and the forms involving sine and cosine functions.
The discussion is ongoing, with participants providing different interpretations of the expression and its simplifications. Some have offered insights into the correct application of Euler's identity, while others are questioning the assumptions made in the simplifications.
There appears to be some confusion regarding the use of Euler's identity and the resulting expressions, with participants highlighting discrepancies in the proposed simplifications. The use of mathematical notation is also mentioned as a point of improvement for clarity.
It doesn't.jaejoon89 said:How does y = e^(x(1-i)) + e^(x(1+i))
work out to y = (e^x)sinx + (e^x)cosx?
Obviously, by Euler's identity, (e^x)sinx+ (e^x)cosx= e^(x(1+i)) only, not that sum.jaejoon89 said:How does y = e^(x(1-i)) + e^(x(1+i))
work out to y = (e^x)sinx + (e^x)cosx?
HallsofIvy said:Obviously, by Euler's identity, (e^x)sinx+ (e^x)cosx= e^(x(1+i)) only, not that sum.