Reduce complex exponential expression

1. Feb 4, 2012

kususe

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).

2. Feb 4, 2012

phyzguy

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. Feb 4, 2012

kususe

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: Feb 4, 2012