couse Information Elementary Linear Aget x C Ngebra question

couse Information Elementary Linear Aget x C Ngebra question I Cheg x e Math 1B03/12cz Summe x Secure www child jonlineform 2.php?assign 5(b) 5 (b) 0/2X 5(b) 5(c) 5(c) Problem #6: Which of the following is a solution to the equation z (1 V3i (A) 21 3[cos(23T/18) i sin 23nt/18)] (B) 1/3 i Sin 8m/9)] (C 2 3[cos (10m/9) i sin( 10mt/9)] 1/3 (D) 2 cos (19m/18) i sin 19nt/18)] (E) 21 (7t/9) i sin 7m/9)] (F) 21 13 18) i Sin 13 t/18)] 1/3 1/3 (G 1/3 +isin 111t/901 (H) 2113[cos(17m/18) i sin( 17m/18) Problem #6: E Just Save Your work has been saved Back to Admin Page) Submit Problem #6 for Grading Problem #6 Attempt Attempt 2 Attempt 13 Your Answer: Your Mark: 0/2X Problem #7: Find the value of 65 V3 65 252 AM Type here to search 2017-U6-0

Solution

z^3 = 1 - sqrt 3 i

z = r cos theta + i sin theta

z^3 = r^3 cos 3 theta + i sin 3 theta

r^3 cos 3 theta + i sin 3 theta = 1 - sqrt 3 i

r = 2

tan 3 theta = - sqrt 3

theta = 2pi/9 , 17pi/9,11pi/9,5pi/9,14pi/9,8pi/9

z = 2^1/3 [ cos (11pi/9) + i sin (11pi/9) ]                option G

z = 2^1/3 [ cos ( 8pi/9 ) + i sin (8pi/9 ) ]                option B