9. Find the complex fourth roots of 81(cos((3π)/(8)) +...

Transcript

00:01 First time we need to turn this complex number into the chick form.

00:06 So one way to do it is we have to find the r here equal to square root of the a square plus b square.

00:15 Then for we should get equal to minus 8 square plus minus 8 square of 3 square.

00:23 Then we'll soon get equal to 64 plus 64 times 3.

00:29 Then we get equal to 192 and plus 64 we get equal to scroll to the 256 so square of the answer equal to 16 so that's i equals 16 now for the second things we need you will be the theta equal to the tension inverse of the minus a squared of 3 divided by minus 8 equal to the tension inverse of the square of 3 and equal to this one will be out of 3 maybe because here we have both i and b in the quadrant 3 here therefore we should get this one this angle theta must equal to pi plus pi out of 3 and we get equal to 4 pi out of 3 therefore we should gain the minus 8 minus 8 i squared of 3 equal to 16 times coside of the 3 4 by out of 3 plus i times side under 4 by out of 3 and here we want to find the the 4 root of the valve of this complex number here so we'll be in quote so we want to find the z barrel 1 out of 4 therefore we should get equal to 16 barrel 1 out of 4 of the coside of 4 pi out of 3 and plus 2 n pi divided by 4 plus i times side of the 4 pi out of 3 plus 2 n pi divided by 4 so for the first case when n equals to 0 which again this one gives us equal to 2 now inside we have the cosine of the 4x8 of 3 and n equals 0 and then we got the 4 bient up of 3 and then we get the pi out of 3 here 5 out of 3 plus i side of the bai out of 3 and we know the cosine by 8 of 3 equals 2 1 1⁄2 plus the size of pi out of 2 equals 2 2 2 2 equals 2 2 2 2 plus square of 3i so that's an equal to 0 for n equal 2 1 we get the next term will equal to 2 cosine of now we have the 4 pi out of 3 plus 2 pi so we should get equal to 10 pi out of 10 pi out of 12 plus i side of 10 pi out of 12 and then we should get equal to 2 10 by out of 12 coside of that will equal to this one will be a 5 pi out of 6 so that will be the cosal of the 5 5 out of 6 it will equal to square of 3 out of 2 and then that's a minus here and plus i time the 5 by out of 6 it will equal to the 1 half and then we will equal to minus square root of 3 plus i and for the case of the n equal to 2 we get the next one we equal to the 2 coside of the now n equals 2 so have 4 times 3 will be 12 and 16 by out of 4 plus out of 12 here, not 4 here.

04:41 Out of 12.

04:42 I size under 16 by out of 12.

04:46 16 out of 12 will equal to 4 out of 3...

Question

9. Find the complex fourth roots of $81\left(\cos\left(\frac{3\pi}{8}\right) + i\sin\left(\frac{3\pi}{8}\right)\right)$.\newline Part I: Find the fourth root of 81. (2 points)

Question

9. Find the complex fourth roots of $81\left(\cos\left(\frac{3\pi}{8}\right) + i\sin\left(\frac{3\pi}{8}\right)\right)$.\newline Part I: Find the fourth root of 81. (2 points)

Please give Ace some feedback