Asked by Tony Thompson
Evaluate ( if multiple values exist write down enough of them to show
a pattern):
(a) sin(iln(i))
(b) (1 + i)^2 + (1 + i)^4
(c) ln(−e)
a pattern):
(a) sin(iln(i))
(b) (1 + i)^2 + (1 + i)^4
(c) ln(−e)
Answers
Answered by
oobleck
sin(ix) = i sinh(x)
sinh(ln i) = (e^lni - e^-lni)/2 = (i - 1/i)/2 = (i+i)/2 = i
so, sin(i lni) = i * i = -1
1+i = √2 cis(π/4), so you have
2cis(π/2) + 4cis(π) = 2i -4
ln(-e) = 1 + πi
sinh(ln i) = (e^lni - e^-lni)/2 = (i - 1/i)/2 = (i+i)/2 = i
so, sin(i lni) = i * i = -1
1+i = √2 cis(π/4), so you have
2cis(π/2) + 4cis(π) = 2i -4
ln(-e) = 1 + πi
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.