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• Lili Ayala

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ELECTROTECNIA NUMEROS COMPLEJOS PRACTICA 7a

EFECTUAR LA OPERACIÓN QUE SE INDICA a) Z = 3 – j4. Hallar ZZ* Z*= 3 + j4 ZZ*= (3 – j4) (3 + j4) ZZ* = (9 + 16) + j(-12 + 12) ZZ* = 25 + j0 b) Z= 10/-40 Hallar ZZ* Z= 10/-40 a = 10*cos(-40) = 7.66 b = 10 sen(-40) = -6.43 Z= 7.66 – j6.43 Z*= 7.66 + j6.43 ZZ* = (7.66 – j6.43) (7.66 + j6.43) ZZ*= (58.67 + 41.34) +j(-49.25 + 49.25) ZZ* = 100.01 + j0 c) Z= 20/53.1 Hallar ZZ* a = 20*cos(53.1) = 12.01 b = 20*sen(53.1) = 15.99 Z= 12.01 + j15.99 Z*= 12.01 - j15.99 Z+Z* = 24.02 – j0

d) Z = 2.5 e-jπ/3. Hallar ZZ* Z = 2.5 cos(π/3) + j 2.5 cos (π/3) Z = 3 + j 3.37 Z* = 3 – j 3.37 ZZ* = (3 + j3.37) (3 – j3.37) ZZ*= (9 + 12.57) +j(-10.11 – 10.11) ZZ* = 21.57 + j0 e) Z = 2 + j8. Hallar Z – Z* Z = 2 + j8 Z* = 2 – j8 Z –Z* = (2 + j8) – (2 – j8) Z –Z* = 0 + j16 f) Z = 10 –j4. Hallar Z + Z* Z = 10 – j4 Z* = 10 + j4 Z + Z* = (10 – j4) + (10 + j4) Z + Z* = 20 + j0 g) ) Z= 95/25 Hallar Z –Z* a = 95*cos(25) = 94.16 b = 95*sen(25) = -12.57 Z –Z* = (94.16 + j12.57) – (94.16 – j12.57) Z –Z* = 0 –j25.14

h) Z = r/θ Hallar Z /Z* a = r*cosθ b = r*senθ Z = r*cosθ + j r*senθ Z* = r*cosθ - j r*senθ

Z/Z* = (r*cosθ + j r*senθ) / (r*cosθ - j r*senθ) Z/Z* =(( r*cosθ)2 – (r*senθ)2) + j (2* r*senθ* r*cosθ)