Reduce complex exponential expression

  • Thread starter kususe
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  • #1
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Homework Statement



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

Homework Equations



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

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
 

Answers and Replies

  • #2
phyzguy
Science Advisor
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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.
 
  • #3
22
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Yes, you're right and the problem was wrong.
In the right-hand side of first expression, there's also

exp(-iwt/2)

And the equivalence is proved.
 
Last edited:

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