# Math Help - real numbers

1. ## real numbers

ok one more quick question.
Find the real part of:
z=e^(1-i (pi/3) )

We just got a handout about imaginary numbers, the prof didn't cover it in class, so I am confused

2. Originally Posted by portstar
ok one more quick question.
Find the real part of:
z=e^(1-i (pi/3) )

We just got a handout about imaginary numbers, the prof didn't cover it in class, so I am confused
$z = {e^{1 - i\frac{\pi }{3}}} = e:{e^{i\frac{\pi }{3}}} = e:\left( {\cos \frac{\pi }{3} + i\sin \frac{\pi }{3}} \right) =$

$= e:\left( {\frac{1}{2} + i\frac{{\sqrt 3 }}{2}} \right) = \frac{{2e}}{{1 + i\sqrt 3 }} = \frac{{2e\left( {1 - i\sqrt 3 } \right)}}{{\left( {1 + i\sqrt 3 } \right)\left( {1 - i\sqrt 3 } \right)}} =$

$= \frac{{2e\left( {1 - i\sqrt 3 } \right)}}{4} = \frac{e}{2} - \frac{e}
{2}i\sqrt 3 \Rightarrow {\text{Re}}\left( z \right) = \frac{e}{2}.$

3. wow. I think I will need to go to the prof to have him explain imaginary numbers to me. yikes.
looking at what you wrote and looking at the worksheet, trying to see how it fits together.. I still don't understand.
Thank you so much though and I will see my prof for help! lol
Thanks!!