Matemáticas Básicas 1

MATEMÁTICAS BÁSICAS. Páginas 285, 286 y 531
Página 285: ejercicios del 9 al 26
9.-6+3i+4+5i
Rectangular
6+3i+4+5i=10+8i
Polar
102+82= 100+64=12.80 θ=tan-1810=45°
10.-5+2i+(7+10i)
Rectangular
5+2i+7+10i=12+12i
Polar
122+122=16.97 θ=tan-11212=45°
11.--8+4i+(2+6i)
Rectangular
-8+4i+2+6i=-6+10i
Polar
(-62)(102)=11.66 θ=tan-110-6=-59°
12.- 5-8i+-7+2i
Rectangular5-8i+-7+2i=-2-6i
Polar
22+62=6.32 θ=tan-162=71°
13.- 3+2i-5+7i
Rectangular
3+2i-5+7i=-2-5i
Polar
-22-52=5.38 θ=tan-162=71°
14.-1+3i-(4+9i)
Rectangular
1+3i-4+9i=-3-6i
Polar
-32-62=6.7 θ=tan-163=63°
15.- -7+3i-(4-2i)
Rectangular
-7+3i-4-2i=-17+8i
Polar
-122+52=13 θ=tan-1512=-22°
16.- -8+4i-9-4i
Rectangular
-8+4i-9-4i=-17+8i
Polar
-172+82=18.78θ=tan-1-817=25°
17.- -3-10i+(2-13i)
Rectangular
-3-10i+2-13i=-1-23i
Polar
-12+232=23.02 θ=tan-1231=87°
18.-4-12i+(-3+16i)
Rectangular
4-12i+-3+16i=-7+4i
Polar
-72+42=8.06 θ=tan-1-47=-29°
19.-4-8i-8-3i
Rectangular
4-8i-8-3i=2-3i
Polar
-42-52=6.4 θ=tan-154=51°
20.- 12-9i-(14+6i)
Rectangular
12-9i-14+6i=2-3i
Polar
22-32=3.6 θ=tan-132=56°
21.- (-1-i)-(-2-4i)=Rectangular:
-1-i
+2+4i
1+3i
Polar:
(1)2(3)2=10=3.16 θ°tan-131=71°

22._(-2-3i)-(-4-14i)=
Rectangular:
-2-3i
+4+14i
2+11i
Polar:
(2)2(11)2= 125= 11.8

θ°tan-1112= 79°

23._(32+13i) + (16 - 34i) =
Rectangular:
32 + 16 +13I - 34I = 18+212 + 4i-9 12I = 2012 - 512I

Polar:

(2012)2(-512)2= 51712 =1.71

θ°tan-1-520 = -14°

24._ (23 - 15i) + (35 -34) =
Rectangular:
195 - 1920iPolar:

(1915)2+ (--1920)2 = 1912= 1.58

θtan-11520 = 37°

25._ (-59 + 35i) =
Rectangular:
-179+ 2330I

Polar:

(-179)2(2320)2 = 2.04

θ°= 2320-179 =69170 =22°

26._ (38 -52) – (-56 + 17I ) =
Rectangular:-1124 - 3714I
Polar:
(-1124)2(3714)2 = 2.68 θ°tan-144477 = 80°

Página 286: ejercicios del 61 al 100
61. (5j)(4j)
20j2=20-1=-20 Rectangular
62. -6j9j
-54j2=-54-1 Rectangular
63. -7j-6
-42j2=-42-1=42 Rectangular
64. -5j-12j
60j2=60-1=-60 Rectangular
65.3j2-5j
6j-15i2
6j+15 Rectangular
152+62=261=16.15 Polar
θ°=tan-1615=21°
66. 7j-9+3j
-21-63j Rectangular
212+632=66.4 Polar
θ°=tan-16321=71°
67. -6j-2-7j
-42+12j Rectangular
-422+122=43.68 Polar
θ°=tan-112-42=-15°
68. -9j-4-5j=45+36j Rectangular
(45)2+(36)2=57.62 Polar
θ°=tan-13645=38°
69. 3+2j5+4j=15+12j+10j+8j2=7+22j Rectangular
(7)2+(22)2=23.09 Polar
θ°=tan-1227=72°
70.4+3j6+j=21+22j Rectangular
(21)2+(22)2=30.41 Polar
θ°=tan-12221=46°
71. 6-2j7-j=40-20j Rectangular
(40)2+(-20)2=44.72 Polar
θ°=tan-1-2040=-26°
72. 8-4j7-2j=48-44j Rectangular
(48)2+(-44)2=65.11 Polar
θ°=tan-1-4448=-43°
73. -3-2j5+6j=-3-28j Rectangular
(-3)2+(-28)2=28.16 Polar
θ°=tan-1-28-3=84°
74. -5-3j2-4j=-22+14j Rectangular
(-22)2+(14)2=26.07 Polar
θ°=tan-114-22=-32°75. 9+6i-1-i
=-9-9i-6i-6i2=-3-15i Rectangular
-32+-152=15.29 Polar
θ=tan-15=79°
=15.29L79°

76. 10+2i-2-i
=-20-10i-2i2-4i=-18-14i Rectangular
-182+-142=22.8 Polar
θ=tan-11418=37°
=22.8L37°

77. 4+5i2
=16+40i+25i2=-9+40i Rectangular
-92+402=41 Polar
θ=tan-1409=-4°
=41L-4°

78. (-5-3i)2
=25-30i+9i2=16-30i Rectangular
162+-302=34 Polarθ=tan-1-3016=61°
=34L61°
79. (-2-4i)2
=4-16i+16i2= -12-16i Rectangular
-122+-162=20 Polar
θ=tan-11612=52°
=20L52°

80. (-3-6i)2
=9+36i+36i2=-27+36i Rectangular
-272+362=45 Polar
θ=tan-136-27=53°
=45L53°
81. (6+7J)(6-7J)
36-42J+42J-49J2=36-49J2=36+49=85 Rectangular
82. (5-7j)(5+7j)
25-49j2=25-49-1=74 Rectangular
83. -1+2j-1-2j
1-4j2=1+4=5 Rectangular
84. -2-4j-2+4j...