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May 28th, 2012, 05:42 AM  #1 
Senior Member Joined: Apr 2010 Posts: 128 Thanks: 0  i don't know how to google is 3=2^x a possible complex no.?
i know complex number got square root 3 such that [ i ] x [ square root +3 ] but is got imagery figures as solutions? 
May 28th, 2012, 06:14 AM  #2 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: i don't know how to google is 3=2^x a possible complex 
July 5th, 2012, 10:56 AM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: i don't know how to google is 3=2^x a possible complex
To extend what Zardoz said, we can represent the number x+ iy as the point (x, y) in the complex plane and then change to polar coordinates r, with and . Further, since we can show that , . Taking the logarithm of that, . But sine and cosine are periodic with period so that for any integer n. And then . That's the reason for the "".


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