real numbers

• Jul 17th 2009, 08:53 AM
portstar
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
• Jul 17th 2009, 09:07 AM
DeMath
Quote:

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

$z = {e^{1 - i\frac{\pi }{3}}} = e:{e^{i\frac{\pi }{3}}} = e:\left( {\cos \frac{\pi }{3} + i\sin \frac{\pi }{3}} \right) =$

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

$= \frac{{2e\left( {1 - i\sqrt 3 } \right)}}{4} = \frac{e}{2} - \frac{e}
{2}i\sqrt 3 \Rightarrow {\text{Re}}\left( z \right) = \frac{e}{2}.$
• Jul 17th 2009, 09:14 AM
portstar
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!!