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Infinite series of complex numbers.

  1. Mar 6, 2006 #1
    I have the two series:
    C = 1 + (1/3)cosx + (1/9)cos2x + (1/27)cos3x ... (1/3^n)cosnx
    S = (1/3) sinx + (1/9)sin2x ... (1/3^n)sinnx

    I have to express, in terms of x, the sum to infinity of these two series.

    Here's what I've done so far:
    Let z represent cosx + jsinx
    C + jS = z^0 + (1/3)Z^1 ... (1/3)^n(Z^n)
    This is a GP with first term 1, common ratio (1/3)Z.
    Sum to infinity of C + jS = a/(1-r) = 3/(3-Z)

    I can't seem to find where to go from there. Can anyone help?

  2. jcsd
  3. Mar 6, 2006 #2


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    Write z=x+iy and break your answer, 3/(3-z) into real and imaginary parts.

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