Asked by Anonymous
Given z=cos*(delta)+j sin*(delta),show that z^n+1/(z^n)=2cos*n*(delta)
Answers
Answered by
Anonymous
,where n is a real number.
Answered by
Steve
to avoid having to use Greek letters, I'll just use x. I think you mean
z = cos(x) + j sin(x)
De Moivre's formula says that
z^n + 1/z^n
= z^n + z^-n
= cos(nx) + j sin(nx) + cos(-nx) + j sin(-nx)
= cos(nx) + j sin(nx) + cos(nx) - j sin(nx)
= 2cos(nx)
cos(x) is a function, not multiplication. Lose the *
z = cos(x) + j sin(x)
De Moivre's formula says that
z^n + 1/z^n
= z^n + z^-n
= cos(nx) + j sin(nx) + cos(-nx) + j sin(-nx)
= cos(nx) + j sin(nx) + cos(nx) - j sin(nx)
= 2cos(nx)
cos(x) is a function, not multiplication. Lose the *
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