Drawing Complex Numbers on a Plane

[Yankel]

Hello all,

I wish to plot and following complex numbers on a plane, and to find out which shape will be created. I find it hard to figure out the first one, I believe that the others will follow more easily (the forth is also tricky).

\[z_{1}=\frac{2}{i-1}\]

\[z_{2}=-\bar{z_{1}}\]

\[z_{3}=\bar{z_{2}}\]

\[z_{4}=\frac{z_{3}}{i}\]

Thank you !

 

[HallsofIvy]

"Rationalize the denominator": \(\displaystyle \frac{2}{i- 1}= \frac{2}{i- 1}\frac{-i- 1}{-i- 1}= \frac{2(-i- 1)}{(-1)^2+ 1}= \frac{-2i- 2}{2}= -i+ 1\)

 

[Yankel]

"Rationalize the denominator": \(\displaystyle \frac{2}{i- 1}= \frac{2}{i- 1}\frac{-i- 1}{-i- 1}= \frac{2(-i- 1)}{(-1)^2+ 1}= \frac{-2i- 2}{2}= -i+ 1\)

you mean -1-i ?

thanks !