Question

Find the 4 fourth roots of 1077 z = COS 9 +isin 107 9 770 و كن. O acis . dis Ob cis 36 57 2370 1677 cis 18 18 9 57 70 2377 87 cis cis cis 36 18 9 137 317 497 677 occis-72 cis-72 cis 72 cis 72 371 57 771 cis cis 4 1377 3171 4971 677 cis cis cis 36 36 36 36 Odcis.cis ** cis Oecis QUESTION 6 3 Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form. (1 - 1)*(41) -2-21 TTTT Paragraph Arial 3 (12p - E - T- co 80 F3 F4 FS % 5 3 4 6 7 8 9

Answer 1

the nth roots of arie Vๆ By De Moiver's theorem z =rcoso tisino) In (cos (2k + 0) +isin (2 kn +og I in = 72 Z a isin 2Kitte n 9 * 1+ 0 n n-1 where k = 0, 1, 2, ..., is in lott is given NU = cos 10 m + of 근 2th roots - is in (2x + 7 ) cos (2k + 10) VA Z 4 k=0, 1, 2, 3 root is For eos is in 100 10 T 9x 4 + 9x4 is in 5 cos 5 T + for k=1 noot is cos 28 T is in 28 7 36 36 cos 70 tisin 7m 9 9 for k= 2, root is - cos 46 T + i sin 46 0 36 cos 23 T tisin 23 18 18 and For k = 3 root is - 36 cos + i sin 64IT 36 36 is in 160 9 cos 160 + 9 roots are So the cis 23 T Cis16th cis 5T 18 cis 7T 9 782 Ams

[-] (1-114 (40)? - 2-2i 16 i (-i)? -2 (1+i) . 16 (1-ig" (1-i 2 (Hi) (1-1) 8. (1-1 1-;? 8(1-1,5 1-1-1) 4.(1-15 1 8(1-195 2 4. [5 (11 7 T isin 75 4.[2 (cos 4 2+5 5 - 2. 7 TT 4 Moiver's theorem ماند (cos tisini (cos 35 in tisin 357 2 4

- 11 [By De Moiver's theorem (3+i)- [2 ( 3 + 1) [2 [cos I tisin II ]] 2" [ cos It is in I 1/4 (3-1) 6 12 3 L 11 Ans 3. 4 i 4