MHB Drawing Complex Numbers on a Plane

AI Thread Summary
The discussion focuses on plotting complex numbers on a plane, specifically the calculations for four complex numbers: z1, z2, z3, and z4. The first number, z1, is calculated as -i + 1 after rationalizing the denominator. The second number, z2, is the negative conjugate of z1, while z3 is the conjugate of z2. The fourth number, z4, involves dividing z3 by i. The participants clarify the calculations and seek to understand the resulting shapes formed by these complex numbers.
Yankel
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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 !
 
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"Rationalize the denominator": [math]\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[/math]
 
HallsofIvy said:
"Rationalize the denominator": [math]\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[/math]

you mean -1-i ?

thanks !
 
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