Question

Consider the following. (7 + 71)(5 – 5i) (a) Write the trigonometric forms of the complex numbers. (Let 0 3 0 < 21.) (7 + 71) = (5-5) = (b) Perform the indicated operation using the trigonometric forms. (Let 0 s@<21.) (c) Perform the indicated operation using the standard forms, and check your result with that of part (b).

Answer 1

S. Given that (7+71), (5-54) Now (a) write the trigonometric form of the above complex number lot 7+7i is in the form of Frigonometre form r(438tisim@3 67€7i) = y(osofi Simo) rcoso=7; & rsino='7 squarsing both side and then add gec650+82 sim ²0= 7² 72 82(Cos?+ Sin ²0) = 2x7² 8² x 1 - 2x72 on otxes as ast=1 tomo = rsimo rcoso 그 it te teho a han itu =0 Flu Now (7+71)= 732 (Cos Vesti Simiyu) Ang Similarly 5-51-r(Cosoti fino) =552 tamo e = since Coro f 316 tano = the value of tano ms -1 is in Quachant il f (V)

afsimo uove So, ten o= And the value of cose is tre" in Quadrant (1) 74 0 - 7174 Then tan 7 15-5i) - 582 (Cos 98%,+ i Simany) past R (b) The indicated operation using the trigomometrie form Y-12-J72+ ze 8=121=752 iz =59 imagenery =-1 fe is angle between de-axes of y-axis (7+34) Daru 415-54), 0 = 774 © these indicated operāliom using the standenen form. (Hery)= x(coso+ismo) Now check- 752 (Cost ute Sinity) 8=782 CosO=Cs Tyu Sim Oz Sim Thu ज ; Sim O= -5 Coso= 'N=7, y=7 (7+71) = 7 12 (5+5) 777 2 (7+71)

la x=5, y=-5, Simo= Sim Talu 4-cheek. (xtaly)=r(Caso te Sino) 82552, Caso = les 77 Caso z Simo S2 5+(-5)=53(titch 5-5) provey es / - 5+5(-1) (5-51) = 15-51)