Using complex numbers to plot coordinates

I'm doing a question on plotting the coordinates of the vertices of a regular pentagon with one Vertex at (minus one, square root 3)
I have used the de moivre theorum and hve tried to use exponential then converted for each angle but only get decimals on the calculator
Is there a method for the exact form?

Reply 1

mqb2766

21

Original post by MayaVellichor

I'm doing a question on plotting the coordinates of the vertices of a regular pentagon with one Vertex at (minus one, square root 3)
I have used the de moivre theorum and hve tried to use exponential then converted for each angle but only get decimals on the calculator
Is there a method for the exact form?

Depending on the side length and the origin, but its just the 5th roots of "unity" so roughly every 2pi/5 on the "unit" circle. Are you told anything else apart from the location of one vertex / can you post the full question.

Guessing that equivalent to the 5th roots of 32 with a rotation to put one at the stated location, or simply mag 2, <2pi/3 + k2pi/5

(edited 5 months ago)

Reply 2

DFranklin

18

Original post by MayaVellichor

I'm doing a question on plotting the coordinates of the vertices of a regular pentagon with one Vertex at (minus one, square root 3)
I have used the de moivre theorum and hve tried to use exponential then converted for each angle but only get decimals on the calculator
Is there a method for the exact form?

Yes, you can do this exactly (but it might not be what you're expected to do).

You can get the other roots by repeatedly multiplying by a 5th root of unity such as (cos 72 + i sin 72). There are actually exact expressions for cos 72 and sin 72 (Google them) so you can do everything with exact calculations.

It will be fairly tedious though. An answer of the form mqb suggests is probably what they want.

Using complex numbers to plot coordinates

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