Question

in the form a + b a) Express the number (3) b) Use the De Moivre's theorem to find (1/2+1/20) (5) c) Find the six sixth roots of -8(ie. find V-B ) and graph these roots in the complex plane (.e. polygonal representation) (8) d) Evaluate i)e". ) ef-1**/2) (write your answer in the form 4+) (4) 201

Answer 1

I have done it for you in detail. Kindly go through.

-1+31 a) (-1+3i)(2-5;) (2+5;) (2 - 5;) 2 + 51 + + -2 +51 + 61+ 15 2 2 2 + 5 13 + lli 29 13 29 29 Since in question picture is not clear, I could not whether it is -1 + 31 - 1 + 31 identify 2+5i 2+ 3 so I am doing both for you. (1 + 3i)(2-3) (2+3;) (2-3;) -1 + 3 2 +31 -2 + 3i+ + 9 2 + 9 7 + 92 13 0- E 7 13 ola 13

b) ( ++;)-z" Izl - ***+6) IN Ho vê arge tant min 174 So 2T/4 á + [Cos T/4 + i sin Sin T/). V2 Now De Moivre's Theorem: To + i sin 1/4] (coso risine)". Cosno +i Sin no, Cat 5;)" (e) (Costly as [Cos 10 +i Sin to I [Cos si ti Sin 5 Cos (217 + 1/2) + i Sin (2T+2)] با 32 2 [ 32 ਭੇੜ 32 [CosT/2 +i Sinal] (o+i] 0+ $zi 32 Li 32

-8. such that we need to find all Let relo we 8 -8 → 6 iso Y e - 8 O-T → recibo it 8e → 6o T + 2n T ; M= 0, 11, 12, - 8 Y = 16 8 (anti) in=0, Il, £ 2,... → be obtained when we different values for co will M= 0, 1, 2, 3, 4, 5. vary it/6 68 e W iT/ 8 wa e W3 8 1571/6 i7 w = 8 e in/6 1372 to e iSiNG 5 68e i "T/6 e woo niya 6/8 e 135/2

iT d) e Cost i Sin T 0 + - + I- 피) - 1 e i72 7 e e 늘 [Cosik [ Cos is + i Sin m/s) - Jo+] e • ㅇ+