Show that the equation $ $ $z^6-i=0$ $ $ is sufficient to define a polygon. Find the area of this polygon.

Question

Show that the equation $ $ $z^6-i=0$ $ $ is sufficient to define a polygon. Find the area of this polygon.

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Would this problem make sense to the average 6th former? (that is, students of 17-18 years old, in their last secondary school year).

Answer 1

No

Show that the equation $z^6-i=0$ is sufficient to define a polygon.

This is a rather meaningless sentence. We all know that the roots of this equation are the vertices of a regular hexagon in the complex plane and so we try to guess what you want to ask. But you didn't ask this.

So no, you should not use such a formulation.

Better say

Show that the roots of $z^6−i=0$ are the vertices of a polygon in the complex plane.

Answer 2

Yes it would. Consider the complex plane and the points defined by the 6 roots of the equation!

Answer 3

HINT: The roots of equation $z^n=a$ are vertices of some figure for $|a|>0$.