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Homework Help: Complex Arithmetic - Mathematica agrees with me, textbook says I'm wrong.

  1. Aug 26, 2012 #1

    Mathematica agrees with my second solution (not the first one though). The back of my textbook says: "[itex]\sqrt[4]{8}[\cos(\frac{5\pi}{8}) + i\sin(\frac{5\pi}{8})][/itex] and [itex]\sqrt[4]{8}[\cos(\frac{13\pi}{8}) + i\sin(\frac{13\pi}{8})][/itex]"

    Edit: The second z in my picture should be |z|, the modulus.

    Edit2: Here are the results from mathematica, confirming that both the textbook AND I are right...


    My question is, how did my textbook get that answer?
  2. jcsd
  3. Aug 26, 2012 #2


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    Staff Emeritus
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    You can get rid of multiples of ##2\pi##. For example, you have
    $$\frac{21\pi}{8} = \frac{(16+5)\pi}{8} = 2\pi + \frac{5\pi}{8},$$ so your first answer is equivalent to the book's first answer. Similarly, you can show your second answer also matches the book's second answer.
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