Exprese los siguientes nmeros complejos en la forma a+bia). (2+3i) + (4+i)=2 + 3i + 4+ i=6 + 4i

b

==

4. demuestre que:a) =)=-2

b) = ======

c)

2.- sean: = 1+i = -2+i = 1-iCalcule lo que se le indique.

1. a = =

1. b = = =

1. c = = =

1. d = = =

1. e = = = =

6.4 ejercicios

a) 5Arcotg=

b)arcog==arcotg=

c)arcotang=

Arcotang==arcotang=e)arcotang=f)

Representa en forma polar los siguientes nmeros complejosa) -4

b) -6i

r=-6a=0

=

c)

60 =1

d) i

e)

f)

g) -2-i

= =2.2360-1

i

h)

==1=36.94 36.96

7. encuentre las races quintas de:a) -8

Encuentre las races quintas de: a) -8Frmula para las races = [cos K = 0, 1, 2, 3, 4n = 5V= = = 80 = 180. + Isen Z 1/5 = 1.6 [cos (36) + isen (36)]Z 1/5 = 1.6 (0.8090 + 0.5877)Z 1/5 = 1.2940 + 0.9403 i

Z 1/5 = ( [cos (Z 1/5 = 1.6 [cos (37.25) + i sen (37.25)Z 1/5 = 1.6 (0.7960 + 0.6052)Z 1/5 = 1.1776 + 0.96832 i

Z 1/5 = ( [cos ( + i sen Z 1/5 = 1.6 (cos (38.51) + i sen (38.51) = 1.6 (0.7824 + 0.6226) (1.25184 + 0.99616 i)

Z 1/5 = [cos( + i sen (Z 1/5 = 1.6 [cos (39.76) + i sen (39.76)Z 1/5 = 1.6 (0.7687 + 0.6395) = 1.22992 + 1.0232 i

Z 1/5 = ( [cos ( + isenZ 1/5 =1.6 (cos (205.13) + sen ( 205.13)Z 1/5 =1.6 (-0.9053 0.4246)Z 1/5 =1.44848 0.67936i

Raz quintaB (1 i)Z = 1- i r = r =r = 1.41420 = arctg = = -10 = -45, 180 45 = 135

Efectue las operaciones indicada:a)==

b) i z010Z n = rn [ cos n 0 + r sen n 0]Z z010 z010 [cos (2010) (90) + i sen (2010) (90)]Zz010 = (1) ) z010 [cos ( 180, 900) + i sen (180, 900)] Z z010 = 1, 005 (-0.9998 0.0157]Z z010 = - 1, 00299 0,0157785i