anonymous
  • anonymous
confuseddd!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
anonymous
  • anonymous
i solved the problem and i got 31.98+0.877i but my online homework says that its wrong D:
anonymous
  • anonymous
multiply the angle by 5!!

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mathteacher1729
  • mathteacher1729
Is this a graded assignment?
anonymous
  • anonymous
i did! look
anonymous
  • anonymous
\[(r(\cos(\theta)+i\sin(\theta))^n=r^n(\cos(n\theta)+i\sin(n\theta))\]
anonymous
  • anonymous
2^5(cos(5.pi/10)+isin(5.pi/10)
anonymous
  • anonymous
ok so you have \[2^5(\cos(\frac{\pi}{2})+i\sin(\frac{\pi}{2}))\] right?
anonymous
  • anonymous
32(cos1571)+isin(1.571)= 32(0.9996)+0.0274i=31.98+0.8768i
anonymous
  • anonymous
so all you need now is \[2^5=32\] and \[\cos(\frac{\pi}{2})=?\]
anonymous
  • anonymous
its pi/10 not 2
anonymous
  • anonymous
put degrees out of your mind. you are working with numbers
anonymous
  • anonymous
\[5\times \frac{\pi}{10}=\frac{\pi}{2}\]
anonymous
  • anonymous
oh ! my bad
anonymous
  • anonymous
now it is easy right?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
whew!
anonymous
  • anonymous
haha thank you! i need help with finding the fourth roots of 256
anonymous
  • anonymous
someone explained me but that's not what im looking for
anonymous
  • anonymous
all four of them right?
anonymous
  • anonymous
yeah like i know the last steps but i dont know to get to the equation, for instance i have this example that i did at school -8+8i , i dont know how to find the r and the angle to have the equation
anonymous
  • anonymous
we can do it the snap way, first find all four roots of 1, then find the fourth roots of 256 one we know already, one fourth root of 256 is 4
anonymous
  • anonymous
ok lets go slowly, but first note that finding the fourth roots of 256 in not like finding the roots of \(-8+8i\) because 256 is real
anonymous
  • anonymous
oh yeah
anonymous
  • anonymous
so all we have to do is find the fourth roots of 1, and then multiply each result by 4
anonymous
  • anonymous
we get two right away, since \(4^4=256\) and also \((-4)^4=256\)
anonymous
  • anonymous
which is like saying \(i^4=1\) and \((-1)^4=1\)
anonymous
  • anonymous
do you know the other two fourth roots of 1?
anonymous
  • anonymous
no
anonymous
  • anonymous
draw a unit circle, you know 1 is one answer so divide up in to 4 equal parts
anonymous
  • anonymous
|dw:1333296129467:dw|
anonymous
  • anonymous
\[1^4=1,i^4=1,(-1)^4=1,(-i)^4=1\] there are the four answers \[\{1,i,-1,-i\}\] distributed evenly about the unit circle in the complex plane
anonymous
  • anonymous
so if i want the 4 "fourth roots" of any number, take those four numbers and multiply by the positive real fourth root for example if i want the fourth roots of 81 i would instantly say: 3, 3i, -3, -3i
anonymous
  • anonymous
why 3?
anonymous
  • anonymous
oh never mind
anonymous
  • anonymous
because \[3^4=81\]
anonymous
  • anonymous
easy right?
anonymous
  • anonymous
yes very haha but im still having problem with the other question the one of cos1/2 , it still says that its wrong

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