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# I have been struggling for the past few hours, help me

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Consider the complex numbers  in the complex plane below:

Some of these complex numbers are 54th roots of unity. Enter those complex numbers in any order, separated by commas. Use the letters to refer to the complex numbers; do not write them in or form.

Apr 3, 2022

#1
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The 54th roots of unity are u, v, and w.

Apr 3, 2022
#2
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I think just v

$$\frac{360}{54}=6.\dot6\; degrees$$

So there will be a 54th root of 1 at 1+0i

then there will be one every 6.666.. degrees around the unit circle.

That graph is split into 24 sectors   360/24 = 15 degrees each

so we need integers such that 15x=6.666.. y     where   x is between 0 and 24 and x and y are both integers

The only one that works is 180 degrees

15*12 = 27*6.6666

So the only answer is v

Apr 4, 2022