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Find all the values of a complex?

I'm struggling to find all the values of this number shown below. The question just states find all the values of this:

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Thank you for any help :smile:


The number is:

ln[16e^(-2*pi*i/17)]
(edited 6 years ago)
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Reply 2
Original post by Charliewiz
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Thank you, I've re-loaded it and typed it out just in case it doesn't work again
Reply 3
Original post by CRD_98
Thank you, I've re-loaded it and typed it out just in case it doesn't work again


There's one "obvious" answer.

Bu then you need to think about the different possible arguments the number you are taking the logarithm of
Reply 4
Original post by RichE
There's one "obvious" answer.

Bu then you need to think about the different possible arguments the number you are taking the logarithm of



Could this be done using ln(z) = ln|z| + iArg(z) ?
(edited 6 years ago)
Reply 5
Original post by CRD_98
Could this be done using ln(z) = ln(z) + iArg(z) ?


Yes, though you mean

ln(z) = ln|z| + iArg(z)
Reply 6
Original post by RichE
Yes, though you mean

ln(z) = ln|z| + iArg(z)


yes thank you, I tried to correct that as soon as a I posted it. Am I right in thinking since z = re^(i.theta) => z = 16 and theta = -2*pi/17

=> ln[16e^(-2i.pi/17)} = ln|16| + i(-2.pi/17 + 2.pi.k) , where kEZ
Reply 7
Original post by CRD_98
yes thank you, I tried to correct that as soon as a I posted it. Am I right in thinking since z = re^(i.theta) => z = 16 and theta = -2*pi/17

=> ln[16e^(-2i.pi/17)} = ln|16| + i(-2.pi/17 + 2.pi.k) , where kEZ


Yep.

No need for |16|. Just 16 will do.

And could write ln16 = 4ln2 if you wanted.
Reply 8
Original post by RichE
Yep.

No need for |16|. Just 16 will do.

And could write ln16 = 4ln2 if you wanted.


That’s great, thank your for all your help :smile:

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