Find all the values of a complex? Watch

CRD_98
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#1
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I'm struggling to find all the values of this number shown below. The question just states find all the values of this:

Attachment 730648




Thank you for any help


The number is:

ln[16e^(-2*pi*i/17)]
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Charliewiz
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CRD_98
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(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
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RichE
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(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
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CRD_98
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(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) ?
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RichE
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(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)
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CRD_98
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(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
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RichE
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(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.
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CRD_98
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(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
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