Question

2. If ze = V15(cos 35° + i sin 35°) and Z2 = v5(cos 10° + i sin 10°), find 777, and write your answers in both trigonometric form and rectangular form. If rounding is necessary, round to three decimal places.

Answer 1

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at ib (Standard foun). rclos Oti sino) (tignonetic form). r= raz+b2 los a sinca b r We have Zz = √5 ( los 2,5 VT5 ( eos 35+ i sin 35'). 10 + i sin 10). Zi= vis Clos 35ti sin 35). ris b cos 35 - 9 sin 35= b 35 ricos 35 = Jis Cod O. = 3.172 b=r. Sin 35= vis sin 35= 2.221 Zia 3.172 +i (2.221) → Sterrelaved four. → Z2 = √5 ( cos lo + i sin 10) b 10 Cos 10 = 9 V5 Sin 10 = b 15 15 az 5. los 10 = 2.202 b= rs. sin 10 0.388 standland foun. 22= 2.202 tic0.385) 2. 202 + (3.172 + 1 (2.220][2 ti 60.388)] Z, Zz ; ²= -1 Note, 1 = [ (3.172 x 2.202) + 3.172 2 1 (0.385) + (2.221)x 2.202 +12(2.221 +0.388)] 6.1229 +66.1213) 1 ZiZ2 = 6.1229 + 6 1213 - Stamelancel form,

teignometria form of Z, Zz in b Z, Z2 = rccos ot i sino) = 8.6579 Ceos 45ti sin45) 12 a temo - b 6. / 229 b= C. 1213. lo= tan b = toñ' E.:1212 ſa2+6² 16.1229?+6.12132 - 44.99 8.6579 45 ZI Zz 3.172 +22211 2-202 + (0.388) at bi a = 3.172 Cadi Erdi) Catbil (e-di) Cordi) = (ac+bd) + (be-ad) i c24d² b= 2.22 C = 2.202 d= 0.388. zi Zz 6.172.2.202 + 2.221.0.356)+(2.221. 2.202 – 3.172.0.388); + 0.3882 2 2.202 21 7.5695 +(0.73 20) - stand and farm Zz un b lignomelic form of Z1/22 fu Z rccos of i sin o) 1.5695 fon ob b= 0.7320. Zz 1.73 18 (los 25 ti sin 25) r= Ja2+62 O=tan' (/) =tan (0.7320 -1.5695) 1.7318 - 25 Result → Z22 = 6-1229+ 6.12 13 = 8.6579 ( cos 45+ ; sin45) 21/22 = 1.5695+ 0.7320 i = 1.7318 (clos 25 + i sin 25)