Question

all of these please

Find the powers of the following complex number. Write your answer in rectangular form. (3/3-3/)* Answer: DO Ovo yo c (03). 응 TE a Check

Answer 1

2 find the indicated roots of the following complex number. write your answer in polar form in degrees Find the cub roof of ( 24 cis (240")) polar Form z = xtiy ie z = 2(coso ti sind) where ja 121 = Argu umente. tant al. s uztyn Solve i e Z the complex number (27 lis (240°)) 27 ( cos (240") + i sin (240")) cub root of 27 cis (240°) is (27 cis (240°)) (27) (cos (240) + i sin (240) thus the z cul اب) } 2 2 - By De, Moivre's theorem + i sin Z will =) 3 ( cos(240) sin (240) 3 ( cos(80%) +i sin (809) 3 ( cos 41 + i sin un therefore the polar formis 3 (cos 47 tising) (Ans).

(3) Find the indicated roots of the following complex number write your answer in polar form in degrees Find the Fourth roof of - 8+813. h where Z = - xting is a polar form. therefore x=-8, y = 853 2). Na 8=.Jartyr T(-8) + (883) 2 [6.4+ 6483 a) 8 = 3) 8 = 8 8 V1+3 r = 8x2 8x2 = 16 의 8 = 16 And 8 - tant 1 1 = 0 = tant 1853 tant (3) 9) tant (tan tan ( =) H 3. therefore the polar form of - 8+8153 is 16fCas(%) +isine) (-8+8i 3t of the polar formis (16) (costo tisin tisin ) Hence

By De, Moivres theorem (1634 2) 8+ (-8 +sir3)+ Geostalih tisin (F) E sivat (24) th (-cost 6-8+8ivgjt therefore the fourth roof of (-8 + 813) (-cos the rising the =) 2 (-Cos 11 h tisin of the polar form is a [-cos th tisinh] find the indicated roots of the following complex number write your answer in polar form in a degree find the Square root of - 4 - 4153 the polar form -z = xtin iez rccos o tisino where rarmayr and o o = tant 13 l Here - 4-4ir la-4, y = – 403 r= JE4g^+ (-4+3) 2 2 516 +1643 =) 482 -8. 78=8 = tant |-er 13 And o= tanta 블 a tano (13) 10 3

Z 8( cost tisins therefore the polar form of square root of (-4-4irg) is (-4-4183) Y (8) /2 (cos of tising) By De, Moivre's theorem (-4-4183) 252 (cos 7 (Ang). therefore the polar form is 212 (cost tisin!) 8=282 (Ang). 1/ tisin ! o = 1