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

  1. Aug 26, 2012 #1
    mathematica.png




    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...

    http://www.wolframalpha.com/input/?i=(1+-+i)^(3/2)+=+(8^(1/4))[cos(45pi/8)+++i+sin(45pi/8)]
    http://www.wolframalpha.com/input/?i=(1+-+i)^(3/2)+=+[8^(1/4)][cos(+13pi/8)+++isin(13pi/8)]

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

    vela

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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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