# Gauss plane set

• September 9th 2011, 04:00 PM
kukov
Gauss plane set
a)The set M= { $z \in C : {z^4}$ + 8 - 8 $\sqrt{3}$i =0 }
Charackterize the set М and point it's the Gauss plane

b)Where exactly is the Gauss plane image from the number z $\in$ for wich is valid:
$\left|\frac{z-1}{z-i}\right|$= 1

Thanks,
Kukov
• September 9th 2011, 09:14 PM
FernandoRevilla
Re: Gauss plane set
Quote:

Originally Posted by kukov
M= { $z \in C : {z^4}$ + 8 - 8 $\sqrt{3}$i =0 } . Charackterize the set М and point it's the Gauss plane

Find $\sqrt[4]{-8+8\sqrt{8}}=\ldots=\{z_0,z_1,z_2,z_3\}$

Quote:

Where exactly is the Gauss plane image from the number z $\in$ for wich is valid: $\left|\frac{z-1}{z-i}\right|$= 1
Equivalently, $|z-1|=|z-i|$ or $d(z,1)=d(z,i)$ and we get the perpendicular bisector of a determined line segment.