# Computmg the powers of a complex number? [closed]

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!

• 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. – Bill Oct 18 at 4:23
• thanks! i got it! – Aran Oct 18 at 18:50

Show[

• @Aran (1/7)*(Cos[Pi/3] + I Sin[Pi/3])^Range[6] // ReIm // ListPlot[MapThread[Callout, {#, Range@6}]] & the effect is the same. – wuyudi Oct 18 at 14:15