- (i+1)^k = -(3^k)
Answer by GusBsAs
(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)i ] = (2m+1)i
=>
k = (2m+1)i / [ (1/2) ln(x) – ln(3) + (2n+1/4)i ]
m,nIf the question were “find k in 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.
- How do I do that? I mean, to me its clear that it converges to 1 (k->infinity), but how do I prove it?
Answer by ecapS trebliH
1 — k/(1+k) = (1+k)/(1+k) — k/(1+k) = 1/(1+k)Therefore | 1 – k/(1+k) | = 1/(1+k)
Now use the definition of convergence. Given epsilon > 0, let N be such that
1/(1+N) 1/epsilon.
Now suppose k > N. Then 1/(1+k) < 1/(1+N) N then | 1 – k/(1+k)| = 1/(1+k) oo) k/(1+k) = 1
- (i+2)^k = -1^k
1 to anything is just 1 so
(i+2)^k = -1
k = log of -1 to the base i+2
Answer by Captain Matticus, LandPiratesInc
(i + 2)^k = -1^k
(i + 2)^k / 1^k = -1Random Casale Media Sponsor AD relevant to bEt365 :
bEt365
((i + 2) / 1)^k = -1
(i + 2)^k = -1
k * ln(i + 2) = ln(-1)
k = ln(-1) / ln(i + 2)
k = log[i + 2](-1)Looks like you got it right enough. However, it should be noted that log(-1) only exists for complex values.
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