Complex number question

Not really sure where to start with this one, I could easily solve it numerically given the ant will walk the path of a regular nine sided shape. But not sure how to achieve the identity that the question requires. Will atta b the question below

OP

q6

Original post by Skiwi

q6

Its very similar to your other recent question. Think about the sum of roots of unity / a geometric series or even solve it geometrically. If you solve it using complex numbers, the distance is given by the magnitude.

(edited 2 years ago)

Reply 3

Skiwi

OP

13

I've reached the required expression this way. Would you say this is the most time efficient method, or is there a quicker way of reaching the solution?

Reply 4

mqb2766

21

Original post by Skiwi

I've reached the required expression this way. Would you say this is the most time efficient method, or is there a quicker way of reaching the solution?

Going down the complex geometric series route, thats about it. You could write it a bit more efficiently at the start as
1 + z + z^2 + z^3
where. .. and the rectangular notation is a bit irrelevant as you're starting at the origin so you simply want the (polar) magnitude as you note at the end. A small (irrelevant) error is that you'd turn to the right (not left) so actually the angle would be negative.

(edited 2 years ago)

Reply 5

Skiwi

OP

13

Original post by mqb2766

Going down the complex geometric series route, thats about it. You could write it a bit more efficiently at the start as
1 + z + z^2 + z^3
where. .. and the rectangular notation is a bit irrelevant as you're starting at the origin so you simply want the (polar) magnitude as you note at the end. A small (irrelevant) error is that you'd turn to the right (not left) so actually the angle would be negative.

Ok thank you.

Complex number question

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