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September 7th, 2010, 08:50 PM  #1 
Senior Member Joined: Sep 2009 Posts: 250 Thanks: 0  Express in a+bi form
Define: Evaluate: My answer (is there a way to make these symbols larger?): Where the ellipses (...) means "What comes next?" or "Is this right so far?" Thanks. 
September 8th, 2010, 03:49 AM  #2 
Senior Member Joined: Sep 2009 Posts: 250 Thanks: 0  Re: Express in a+bi form
Same exact post, but a little bit more readable. Define: Evaluate: My answer (is there a way to make these symbols larger?): Where the ellipses (...) means "What comes next?" or "Is this right so far?" Thanks. 
September 10th, 2010, 06:49 PM  #3 
Joined: Aug 2010 Posts: 48 Thanks: 0  Re: Express in a+bi form
Hi, I am just thinking about the word "evaluate"... does it mean simplify or something? In which sence? I found the original expression pretty simple... Best regards, Jens 
September 10th, 2010, 07:04 PM  #4 
Joined: Aug 2010 Posts: 48 Thanks: 0  Re: Express in a+bi form
Replying myself... just an idea. Why you don't use the normal decomposition I mean, looks not that bad ...and again, me idiot: I should have read the header in this case. Damn... Best regards, Jens 
September 11th, 2010, 10:22 AM  #5  
Senior Member Joined: Sep 2009 Posts: 250 Thanks: 0  Re: Express in a+bi form Quote:
The trick was to use Euler's formula, which says: The other trick was to work out this case of Euler's formula: like this (if you can read this teeny print): or even easier, using trig identites: Then, you can get the final answer from this point: by substituting for all four exponentials, and then simplifying (I'm not sure I did all of this right):  
September 12th, 2010, 06:01 PM  #6 
Senior Member Joined: Sep 2009 Posts: 250 Thanks: 0  Re: Express in a+bi form
I posted too soon. There is an error in that last post. You can't expand using Euler's formula. This is the whole problem with, I think, no mistakes: Define: Evaluate: Use Euler's formula: Solution (I think): That's as simplified as I can get it. There is no imaginary component. 
October 6th, 2010, 07:18 PM  #7 
Joined: Dec 2009 Posts: 150 Thanks: 0  Re: Express in a+bi form
let c = a + i*b where a and b are real. then Giving us the more aesthetically pleasing answer (in z = Re(z) + i*Im(z) form): The cosh and sinh are hyperbolic functions, which are defined by the exponential substitutions I utilized to get to the last step. http://en.wikipedia.org/wiki/Hyperbolic_function 
October 7th, 2010, 07:06 AM  #8 
Joined: Dec 2009 Posts: 150 Thanks: 0  Re: Express in a+bi form
I just noticed I somehow forgot the b in the expansion (where a and b are real valued) , so wherever you see in the above it should be . The final answer is thus supposed to be 

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