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August 18th, 2017, 08:43 AM  #1 
Newbie Joined: Aug 2017 From: Milan Posts: 3 Thanks: 0  Best way to solve this complex equation
Hello everybody, which is the best way to solve (z*  1/z)(z^2+8z*)=0 ? (z* is z conjugate) thank you 
August 18th, 2017, 09:28 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,009 Thanks: 1042 
if the product equals zero then one or more of the factors must equal zero. Solve that for both factors. For example $z^*  \dfrac 1 z = 0$ $z^* = \dfrac 1 z = \dfrac {z^*}{z^2}$ so $z^2=1$ and thus this is satisfied for any point on the unit circle. You try the second factor. 
August 30th, 2017, 06:01 PM  #3 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,390 Thanks: 100  
September 2nd, 2017, 07:49 AM  #4 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,390 Thanks: 100  

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