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Math Help - im & re as functions of x & y - complex analysis

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    im & re as functions of x & y - complex analysis

    Find the real and imaginary parts of the following functions as functions of x and y.

    (i) z^3
    (iii) (z+z^{-1}) \ (z\ne 0)
    (vi) {1\over 1-z} \ (z\ne 1)
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  2. #2
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by JJMC89 View Post
    Find the real and imaginary parts of the following functions as functions of x and y.

    (i) z^3
    (iii) (z+z^{-1}) \ (z\ne 0)
    (vi) {1\over 1-z} \ (z\ne 1)
    1  (x+iy)^3 solve and group numbers with "i" and without it so those with "i" will be imaginary ones ...

    2  \displaystyle (x+iy) + \frac {1}{x+iy} add those than multiply with  \displaystyle \frac {x-iy}{x-iy} and than group Re and Im

    6  \displaystyle \frac {1}{1-x - iy } this one multiply with \displaystyle \frac {1-x+iy}{1-x+iy} than do same thing
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    Note that \text{Re}(z+w)= \text{Re}(z)+ \text{Re}(w).

    So  \text{Re}(z+z^{-1})=x+\frac{x}{x^2+y^2}.
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