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Homework Help: Calculating complex number

  1. May 19, 2008 #1
    [SOLVED] calculating complex number

    1. The problem statement, all variables and given/known data

    Calculate [tex]{i}^{\frac{3}{4}}[/tex]

    2. Relevant equations



    3. The attempt at a solution

    I tried with

    [tex]i=cos\frac{pi}{2}+isin\frac{\pi}{2}[/tex]

    [tex]i^3=cos\frac{3pi}{2}+isin\frac{3\pi}{2}[/tex]

    [tex]i^3=-i[/tex]

    [tex]\sqrt[4]{i^3}=\sqrt[4]{-i}[/tex]

    I don't know where I should go out of here. Please help!
     
  2. jcsd
  3. May 19, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Why don't you just go all the way at once? i=e^(i*pi/2). So i^(-3/4)=(e^(i*pi/2))^(-3/4). Now use laws of exponents. Notice this answer isn't unique. i is also equal to e^(i*(pi/2+2pi)=e^(i*5pi/2). This is the same sort of nonuniqueness you get with square roots.
     
  4. May 20, 2008 #3
    Thanks. I solve it.
     
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