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this is the complex number im dealing with

    zb=(1/7)* (Cos[Pi/3]+I Sin[Pi/3])

I need to represent for the first 10 powers in the plane. I also need to label the points with "z to the power n(n is the power for which i elevate zb)

I need to label the axes, I need to do all this in mathematica

My questions

  1. How can I represent a complex number in mathematica
  2. How can I represent for the first 10 powers the plane.
  3. How can I label each point on the graph to the corresponding power?

my professor gave me a hint to use the callout[] command in mathematica. thank you!

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  • $\begingroup$ 1. zb=1/7*(Cos[Pi/3]+I*Sin[Pi/3]2. Look up Re and Im in the documentation. Then try something like ListPlot[{Re[zb],Im[zb]] Look up Table in the documentation. Those should be enough of a hint to get you started on your own. $\endgroup$ – Bill Oct 18 at 4:23
  • $\begingroup$ thanks! i got it! $\endgroup$ – Aran Oct 18 at 18:50
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Show[
    (1/7)*(Cos[Pi/3] + I Sin[Pi/3])^Range[6] // ReIm // 
        ListPlot[ # -> Range@6] &,
    (1/7)*(Cos[Pi/3] + I Sin[Pi/3])^Range[7, 10] // ReIm // 
        ListPlot[# -> Range[7, 10], LabelingFunction -> Above] &
    ]

enter image description here

| improve this answer | |
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  • $\begingroup$ how can I label the points with the phrase "z to the power n(n corresponding from 1 to 10) $\endgroup$ – Aran Oct 18 at 12:22
  • $\begingroup$ Table[Callout[z1^n, Row[{"z to the power ", n}]], how could i make this work? thank you $\endgroup$ – Aran Oct 18 at 12:23
  • $\begingroup$ @Aran (1/7)*(Cos[Pi/3] + I Sin[Pi/3])^Range[6] // ReIm // ListPlot[MapThread[Callout, {#, Range@6}]] & the effect is the same. $\endgroup$ – wuyudi Oct 18 at 14:15

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