Numeros complejos

MANTENIMIENTO ELECTRONICO E INSTRUMENTAL INDUSTRIAL

NÚMEROS COMPLEJOS

1. Convierta lo siguiente de la forma rectangular a la polar:
a. 4 + j3
a=4
b=3
=arc tg 3/4 = 36.87

b. 2 + j2
a=2b=2
=arc tg 2/2 = 45

c. 7.6 – j9
a=7.6
b=9
=arc tg 9/7.6 = 11

d. –8 + j4
a=-8
b=4
=arc tg 4/-8 = -9.49

e. –5.6 + j86

a=-5.6
b=86
=arc tg 86/-5.6 = -15.9

2. Convierta losiguiente de la forma polar a la rectangular:

a. 6[pic]30°
a= cos 6[pic]30° a=0.99
b= sen 6[pic]30° b=0.11
0.99+0.11j

b. 40[pic]80°
a= cos 40[pic]80°a=0.75
b= sen 40[pic]80° b=0.66
0.75+0.66j

c. 7.52[pic]–125°
a= cos 7.52[pic]–125° a=-124
b= sen 7.52[pic]–125° b=124.86
124+124.86j

d.1.2[pic] 135°
a= cos 1.2[pic] 135° a=0.99
b= sen 1.2[pic] 135° b=0.066
0.99+0.06j

e. 0.008[pic] 310°
a= cos 0.008[pic] 310° a=0.99
b= sen0.008[pic] 310° b=0.09
0.99+0.09j

3. Realice las siguientes operaciones de suma y resta:
Suma de dos números complejos
[pic]

a. (4.2 + j6.8) + (7.6 + j0.2)(4.2+7.6)+(6.8+0.2)j = 11.8+7j

b. (9.8 + j6.2) – (4.6 + j4.6)
(9.8-4.6)+(6.2-4.6)j = 5.2+1.6j

c. 6[pic]20° + 8[pic]80°
15[pic]40°

d. 42[pic]45° + 62[pic]60° – 70[pic]120°33[pic]45°

4. Realice las siguientes operaciones de multiplicación y división:
PRODUCTO DE NUMEROS COMPLEJOS
[pic]

a. (2 + j3)(6 + j8)
(2 + j3)(6)+ (2 + j3)(8j)12+18j+16j+24j[pic]
12+34j+24(-1) = 12+34j-24
-12+34j

b. (7.8 + j1)(4 + j2)(7 +j6)
(7.8 + j1)(4)+ (7.8 + j1)(2j)
31.2+4j+15.6j+2j[pic] = 31.2+19.6j+2(-1)
(29.2+19.6j)(7)+(29.2+19.6j)(6j)
204.4+137.2j+175.2j+117.6 j[pic]
204.4+312.4j+117.6(-1)
86.8+312.4j

c. (2[pic]60°)(4[pic]22°)
13[pic]6°

d. (6.9[pic]8°)(7.2[pic] –72°)...