Loser66
  • Loser66
Find z such that tanz = i/2 Please, help
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Loser66
  • Loser66
My attempt: \(tan z = \dfrac{sin z}{cos z}=\dfrac{e^{iz}-e^{-iz}}{2i} *\dfrac{2}{e^{iz}+e^{-iz}}=\dfrac{i}{2}\)
Loser66
  • Loser66
hey, faking girl, help me out. hehehe
dan815
  • dan815
|dw:1444248216913:dw|

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Loser66
  • Loser66
\(e^{2iz}=1/3\)
dan815
  • dan815
|dw:1444248414375:dw|
Loser66
  • Loser66
from above \(2(e^{iz} -e^{-iz}) = -(e^{iz}+e^{-iz})\) \(2e^{iz}-2e^{-iz}+e^{iz}+e^{-iz}=0\) \(3e^{iz}-e^{-iz}= 0\)
Loser66
  • Loser66
multiple both sides by \(e^{iz}\), we get \(3e^{2iz} -1=0\\e^{2iz} = 1/3\)
dan815
  • dan815
|dw:1444248554037:dw|
Loser66
  • Loser66
ok, you do your work, I do mine. then compare, hehehe. it's fun
dan815
  • dan815
|dw:1444248655592:dw|
Loser66
  • Loser66
2iz = log (1/3) the RHS : \(log (1/3) = log|1/3| + i(arg (1/3) +2k\pi): k\in \mathbb Z\)
dan815
  • dan815
|dw:1444248766740:dw|
Loser66
  • Loser66
now combine LHS \(z =\dfrac{log|1/3| + i arg(1/3+2k\pi)}{2i}=\dfrac{arg(1/3 + 2k\pi}{2} -\dfrac{ilog|1/3|}{2} \)
Loser66
  • Loser66
You missed the real part!!!
Loser66
  • Loser66
As what you draw, z has real part, right? is it not just imaginary.
Loser66
  • Loser66
Yeah, you solve for y only, while z = x + iy.
dan815
  • dan815
=]
dan815
  • dan815
z is real in e^iz
dan815
  • dan815
e^itheta = cos theta + i sin theta there there is real
dan815
  • dan815
where theta* is real
anonymous
  • anonymous
wow i must be dumb i dont get this at alll xD
anonymous
  • anonymous
im 14 and in 11th grade but i dont get this
anonymous
  • anonymous
You must teach me so i can master it
anonymous
  • anonymous
Teach me
anonymous
  • anonymous
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Loser66
  • Loser66
hahaha.... I am not a teacher, how can I teach you, ask "Honor professor dan815" please

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