Recent content by CTID17

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    Laurent Series of 1/[(z-i)(z-2)] at z0=i

    Thanks a lot . I was doing the same thing, except I've forgotten about geometric series :) . Got it now :) .
  2. C

    Laurent Series of 1/[(z-i)(z-2)] at z0=i

    Homework Statement Find the Laurent series at z0=i, which is convergent in the annulus A ={z:0<|z-i|<51/2 } of 1/[(z-i)(z-2)] Homework Equations The Attempt at a Solution |z-i|/51/2 <1 i make 1/[(z-i)(z-2)] = 1/[51/2 (z-i)((i-2)/51/2 + (z-i)/51/2 ) now how do i make it...
  3. C

    Complex Variables: Need help with Chebyshek poly and de Moivre Theorem

    Thank you!
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    Complex Variables: Need help with Chebyshek poly and de Moivre Theorem

    Re(z) = (z+conjugate z)/2 z = [cos(arccos(x)) + isin(arccos(x))]^n conjugate z = [cos(arccos(x)) - isin(arccos(x))]^n now, do i simplify z into z= [x+ isqrt(1-x^2)]^n and conjugate z = [x- isqrt(1-x^2)]^n ? if i keep them in polar form, i get...
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    Complex Variables: Need help with Chebyshek poly and de Moivre Theorem

    Homework Statement The nth order Chebyshev polynomial is defined by Tn(x)= cos( n arccos(x) ) , n is a positive integer; -1<= x <= 1. Using the de Moivre theorem, show that Tn(x) has the polynomial representation Tn(x)= 1/2 [(x+sqrt(x2-1))n+(x-sqrt(x2-1))n] The Attempt at a Solution I really...
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