My Math Forum Best way to solve this complex equation

 Complex Analysis Complex Analysis Math Forum

 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: 2,530 Thanks: 1390 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
Banned Camp

Joined: Mar 2015
From: New Jersey

Posts: 1,720
Thanks: 126

Quote:
 Originally Posted by romsek if the product equals zero then one or more of the factors must equal zero.
True for real numbers. You should show it's true for complex numbers- simple but not obvious.

September 2nd, 2017, 07:49 AM   #4
Banned Camp

Joined: Mar 2015
From: New Jersey

Posts: 1,720
Thanks: 126

Quote:
 Originally Posted by zylo True for real numbers. You should show it's true for complex numbers- simple but not obvious.
$\displaystyle z_{1}z_{2}=0 \rightarrow z_{1}$ and/or $\displaystyle z_{2}=0$ is not only obvious but trivial: z has an inverse if $\displaystyle z \neq 0$

My apologies.

 Tags complex, equation, solve

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post wortel Linear Algebra 2 November 30th, 2015 08:51 PM wortel Math 2 November 17th, 2015 02:26 PM farewell Algebra 5 September 27th, 2014 12:46 PM rayman Complex Analysis 5 October 27th, 2013 10:17 PM watanuki Complex Analysis 1 October 24th, 2009 07:37 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top