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Square root of i and -i

  1. Dec 20, 2013 #1
    1. The problem statement, all variables and given/known data
    The value of √i + √-i , where i=√-1 is
    (a) 0 (b) 1/√2 (c) √2 (d) -√2

    Only one option can be chosen

    2. Relevant equations



    3. The attempt at a solution

    Let (x + iy)2=i
    Solving for x and y, I got
    √i = +1/√2 (1+i) or -1/√2 (1+i)

    Similarly i got
    √-i = +1/√2 (1-i) or -1/√2 (1-i)

    Now how do I calculate, √i - √-1,
    i.e since there 2 possible values for each √i and √-i , which do i subtract from which?

    Using another method I got the final nswer as + or - √2 , but u can only choose one of the given options
     
  2. jcsd
  3. Dec 20, 2013 #2

    D H

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    They are asking for the principal square root.
     
  4. Dec 20, 2013 #3
    How are principal square roots defined for imaginary numbers?
    For eg, if you have 1 - i and -1 + i as the 2 square roots, which do you choose as the principal one?
    If you have i and -i, which do you choose?
     
  5. Dec 20, 2013 #4

    vela

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    Education Advisor

    Have you tried looking up the definition in your textbook or notes?
     
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