anonymous
  • anonymous
Find the quotient z/w if z=12[cos(5pi/18) +isin(5pi/18)] and w=4[cos(7pi/36) +isin(7pi/36)]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
why dont you first transform them into the form \[r*e^{(i*\Theta)}\]
anonymous
  • anonymous
then you would have fraction of exponents so you would just substract the exponents
Loser66
  • Loser66
@Lills knock,knock understand what he means?

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anonymous
  • anonymous
My Internet went out, but I'm not exactly sure what he means
anonymous
  • anonymous
subtract the angles
anonymous
  • anonymous
\(12\div 4=3\) and \(\frac{5\pi}{18}-\frac{7\pi}{36}\) will give you the angle you need
anonymous
  • anonymous
that is why this easy and not hard it is just a subtraction problem
Loser66
  • Loser66
but the condition is student know what the Euler number is, hehehe. me not for example
anonymous
  • anonymous
??
anonymous
  • anonymous
I'm not quite sure i understand
Loser66
  • Loser66
hahahaha..... that can be foreseen.
anonymous
  • anonymous
in plain english subtract the angles when you divide
anonymous
  • anonymous
Like how to write the final answer
anonymous
  • anonymous
\[r_1\left(\cos(\theta)+i\sin(\theta)\right)\div r_2\left (\cos(\alpha)+i\sin(\alpha)\right)\] \[=\frac{r_1}{r_2}\left (\cos(\theta-\alpha)+i\sin(\theta-\alpha)\right)\]
anonymous
  • anonymous
in your case \(12\div 4=3\) so that goes out front
anonymous
  • anonymous
your next job is only to compute \[\frac{5\pi}{18}-\frac{7\pi}{36}\]
anonymous
  • anonymous
i totaly forgot about that formula , i guess hes supposed to use that formula not convert
anonymous
  • anonymous
right it is just a subtraction problem that is all
Loser66
  • Loser66
Please, first off, the asker has to know about Euler formula. what if he/she didn't know about it?
anonymous
  • anonymous
no
anonymous
  • anonymous
divide the modulus subtract the anglers that is all
anonymous
  • anonymous
So the final answer would be 3(cos(pi/12)+isin(pi/12) ?
anonymous
  • anonymous
yes, that is it
anonymous
  • anonymous
easy right? boils down only to dividing 12 by 4 and subtraction that is why you write complex numbers in this form makes the calculation really really easy
anonymous
  • anonymous
Yes thank you so much for your help tonight!

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