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Homework Help: Reduce complex exponential expression

  1. Feb 4, 2012 #1
    1. The problem statement, all variables and given/known data

    prove that:
    1-exp(-iwt)= 2i*sin(wt/2)

    2. Relevant equations

    exp(iwt)= cos (wt) + i*sin(wt)

    3. The attempt at a solution

    I attempted to express the exponential into sum of cos and sin and considering t=2*t/2 in order to obtain an argument like (t/2) (using duplication expression of trigonometry theory).

    Thanks in advance
  2. jcsd
  3. Feb 4, 2012 #2


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    Science Advisor

    You must have the problem wrong, because the equation you are trying to prove is not true. For example, if wt = pi/2, then the left-hand side is equal to 1+i and the right-hand side is equal to √2 * i.
  4. Feb 4, 2012 #3
    Yes, you're right and the problem was wrong.
    In the right-hand side of first expression, there's also


    And the equivalence is proved.
    Last edited: Feb 4, 2012
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