Find all complex cube roots of 27.

greatwhiteshark said:
Find all complex cube roots of 27.
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They all have magnitude 3
They are separated by (360º/3) = 120º
One of them is the Real Number 3.

This should seem familiar.
 
no

It is not familiar. Soroban helped with this one. Soroban takes time to explain my questions one step at a time. Your hints are not always helpful.
 
Expecting you to think it through is not unreasonable.

You have DeMoivre's Theorem. Simply apply it.

27 =
27 + 27*i*0 =
27*cos(0º) + 27*i*sin(0º) =
27*cis(0º)

[27*cis(0º)]^(1/3) =

[27^(1/3)]cis(0º/3 + n*360º/3) = (3)cis(0º + n*120º)for n in {0,1,2}, giving:

3*cis(0º), 3*cis(120º), 3*cos(240º)

cis(120º) = cos(120º)+i*sin(120º) = (1/2) + i*[sqrt(3)/2]

That's enough hints. You do the rest.
 
It IS much MORE. I'm not so sure how much BETTER it is.

Which version requires you to think? That would be the one of greater value, in my view.
 
Jolly, I count 248 posts (and who knows how many under different screen names), all without any indication of any effort on the part of GWS. There comes a point where one must wonder if any benefit is being achieved. It does seem to be an excellent way to write the answer key to several textbooks. Occasionally, I try something different just to see if a useful reply can be obtained. I believe GWS does not like my "other" approach.

GWS, reread the rules for participation. This is NOT a place to get someone else to do your work for you. Blanket bombing problems will NOT EVER be as beneficial as struggling in your own mind in an effort actually to make sense of what is required of you. Do you learn the material presented to you? We cannot tell because you do not show us. Do you pass your exams? We cannot tell, because we do not know where your endless problems come from. Are we passing your exams for you? You WILL regret that. I would find it truly comforting, filling me with warm, fuzzy feelings, if you would present your problems like this:

I got this one:

(then show your completed work}

But this one seems to be different:

{then show your incomplete work}.
 
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