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    I need to expand the funtion cos(z) in taylor series at arbitrary point w belonging to complex numbers. It says to use the addition formula. Z also belongs to complex. So far i hv written out cos(z) = cos(z-w+w) then used addition formula to expand but i'm not sure what to do next, partly because i don't fully understand why i hv to use addition formula, why can't i just use formula for taylor series about a point?
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    (Original post by Ishika)
    I need to expand the funtion cos(z) in taylor series at arbitrary point w belonging to complex numbers. It says to use the addition formula. Z also belongs to complex. So far i hv written out cos(z) = cos(z-w+w) then used addition formula to expand but i'm not sure what to do next, partly because i don't fully understand why i hv to use addition formula, why can't i just use formula for taylor series about a point?
    Complex analysis, I think I remember having the same question as that. You can't just you the formula around a point simply because cos(z) doesn't equal cos(z-w). Hence you have started right, you just the addition formual to expand and simplify are you are done.
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    After i expand then i hv terms cos(z-w)cozw - sin (z-w)sin(w).
    Then do i just expand cos(z-w) using taylor series or maclaurin series?
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    The answer i get is the same as the series expansion for cosz but with z=z-w. Why coudn't i have used the series expansion in the beginning?
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    Could it be that it means writing \cos{z} = \cos\left(a+ib\right) and using the addition formula on that?
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    There's very little point in doing that - the standard series \displaystyle \cos z = 1 - \frac{1}{2!} z^2 + \frac{1}{4!} z^4 - \cdots works just as well for complex z as for real z.
 
 
 
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