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Find the branch points of the function f(z) = (z4 −1)1/4. Draw a set of branch cuts for this function to make this function single-valued in the complex plane. |
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Answer» The branch points of this function are at z = 1, i, −1, −i . As z → ∞, f(z) → z(1 − z −4/4 + · · ·). Thus z∞ is not a branch point of the function. We draw straight lines joining 1 to i , i to −1 , and −1 to −i , and the function is single-valued in the cut-plane |
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