Yahoo Answers: Answers and Comments for Solve for k. With imaginary number.? [Mathematics]
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From Delilah
enUS
Tue, 30 Apr 2013 17:55:32 +0000
3
Yahoo Answers: Answers and Comments for Solve for k. With imaginary number.? [Mathematics]
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https://answers.yahoo.com/question/index?qid=20130430175532AAT6Ffy
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From Theo: zxd
https://answers.yahoo.com/question/index?qid=20130430175532AAT6Ffy
https://answers.yahoo.com/question/index?qid=20130430175532AAT6Ffy
Mon, 21 Jul 2014 18:08:33 +0000
zxd

From GusBsAs: (i+1)^k = (3^k)
=>
((1+i)/3)^k = 1
=&g...
https://answers.yahoo.com/question/index?qid=20130430175532AAT6Ffy
https://answers.yahoo.com/question/index?qid=20130430175532AAT6Ffy
Sat, 04 May 2013 14:51:02 +0000
(i+1)^k = (3^k)
=>
((1+i)/3)^k = 1
=>
ln[((1+i)/3)^k] = ln(1)
=>
k ln((1+i)/3) = ln(1)
=>
k [ (1/2) ln(x)  ln(3) + (2n+1/4)πi ] = (2m+1)πi
=>
k = (2m+1)πi / [ (1/2) ln(x)  ln(3) + (2n+1/4)πi ]
m,n ∊ ℤ
If the question were "find k in ℕ such that...", the answer wpuld be "it is not possible", because the absolute value of the left side is 2^(k/2) and the abs. v. of the right side is 3^k, and a power of 3 cannot be equal to a power of 2, except if k=0, but in this case the left side is 1 and the right side is 1.