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anonymous
 one year ago
Thanks for helping!
I need to simplify this equation to a+bi form.
(1/2(cos(72 degrees)+isin(72 degrees))^5
To solve I should do 1/2^5 and multiply 72 degrees by 5 right? Thanks for helping!
anonymous
 one year ago
Thanks for helping! I need to simplify this equation to a+bi form. (1/2(cos(72 degrees)+isin(72 degrees))^5 To solve I should do 1/2^5 and multiply 72 degrees by 5 right? Thanks for helping!

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 @ganeshie8 @Nnesha @wio @abb0t @zepdrix @Whitemonsterbunny17 @mathmate @jagr2713 @iki @Mehek14 @ikram002p

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0multiply \(72\) by \(5\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so if I do that and simplify it is right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you also have to take \(\left(\frac{1}{2}\right)^5\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if by "simplify" you mean "evaluate the functions" then yes

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yup, that is what I meant

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@satellite73 Can you help me find the complex fifth roots of 55sqrt(3)*i?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah first write \[55\sqrt{3}i\] in trig form do you now how to do that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0r=sqrt((5)^2+(5sqrt(3)^2)) for r

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and 5sqrt(3)/5=tan(theta) for theta

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and then I make a rcis(theta)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah \(r=\sqrt{a^2+b^2}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0from there what do I do?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0did you find \(\theta\)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0theta=pi/3 Sorry for being a little late. My browser froze :(

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah looks like you got it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0From there how do I fin the complex fifth roots?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0divide the angle by 5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do I get the 5th root of r?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0just say it \[\sqrt[5]{10}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you can't really evaluate any of this, just write it in trig form

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is there more to it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It asks me for the complex fifth roots

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0there are five of them

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0go around the circle again, then repeat

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so I add 2pik to the angle?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right, the original angle then divide by 5 again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0or else you can divide the circle in to 5 equal parts, with \[\frac{\pi}{15}\]as one of them

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0each time I add +2pi, should I divide r by 5, or is that a one time thing?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0add \(2\pi\) to \(\frac{\pi}{3}\) then divide that one by \(5\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh, does r change at all?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no it is going to be \(\sqrt[5]{10}\) each time

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh wait, i think your \(r\) is wrong, check it again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So would the first one be \[\sqrt[5]{10}(cis(\pi/3))?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Are you sure, I got 10 again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sqrt{5^2+(5\sqrt{3})^2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it's okay, you're the one helping me :) Would the first answer be \[\sqrt[5]{10}(cis(\pi/3))\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it's fine he is still viewing the chat so just give him a minute or to

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh sorry was away for a minute

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok you found \(r=10,\theta =\frac{\pi}{3}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is the thing I wrote earlier correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so \[55\sqrt{3}i=10\left(\cos(\frac{\pi}{3})+i\sin(\frac{\pi}{3})\right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you want the five fifth roots

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sqrt[5]{10}(cis(\pi/3))?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0one is \[\sqrt[5]{10}\left(\cos(\frac{\pi}{15})+i\sin(\frac{\pi}{15})\right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then add \(2\pi\) to \(\frac{\pi}{3}\) to get \(\frac{5\pi}{3}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yeah , what you said

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0divide by 5 and the next one is \[\sqrt[5]{10}\left(\cos(\frac{\pi}{3})+i\sin(\frac{\pi}{3})\right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure what you mean

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you divided without adding 2pik where k=1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we now have two fifth roots (3 more to go) one is \[\sqrt[5]{10}\left(\cos(\frac{\pi}{15})+i\sin(\frac{\pi}{15})\right)\] and the other is \[\sqrt[5]{10}\left(\cos(\frac{\pi}{3})+i\sin(\frac{\pi}{3})\right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I can +4pi and divide by 5 for another one?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh no we did add \(2\pi\) to the original angle of \(\frac{\pi}{3}\) to get \(\frac{5\pi}{3}\) then we divided that one by 5 to get \(\frac{\pi}{3}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0or add \(2\pi\) to \(\frac{5\pi}{3}\) same thing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0when you add you get \(\frac{11\pi}{3}\) divide that by 5 and get \(\frac{11\pi}{15}\) for the third root

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lather, rinse, repeat

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0don't add \(2\pi\) to \(\frac{11\pi}{15}\) add it to \(\frac{11\pi}{3}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hold on a second, it is not a mystery why you are doing this both sine and cosine are periodic with period \(2\pi\) that means the angle is NOT unique

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so all the original numbers are the same \[55\sqrt{3}i=10(\cos(\frac{\pi}{3})+i\sin(\frac{\pi}{3}))=10(\cos(\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))=...\] then are all equal

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you are just expressing the original number in trig form with different values of \(\theta\) then you divide each of them by 5 to get the different fifth roots

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yup, so I just continue doing what we were just doing?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the theta of the roots would be pi/15, pi/3, 11pi/15, 17pi/15, and 23pi/15?
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