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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: 2,430 Thanks: 1315 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
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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
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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.

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