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Números complejos y cálculo diferencial de una variable
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Apuntes acerca de números complejos y funciones de una variable
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, i i i i iMago ago Mang 9g EN
NÚMEROS COMPLEJOS Y CÁLCULO DIFERENCIAL DE FUNCIONES DE UNA VARIABLE
NÚMEROS COMPLEJOS
• Se denomina unidad imaginario al número i = Fa
•
En la expresión
✗
z
yi
= +
✗, EIR forma Dinámica número complejo
y es la del 2 .
/
→
✗ es la parte real de 2 se derrota ✗ = Re (2)
y
Im ( a )
→
Y =
de 1m ( )
m-f.iy.pe
y
es La
parte imaginario 2
y se derrota 2 = z -
31-5 ,
'
Z =
,
- - - . •
-
i
El (
_
conjunto de números complejos derrota !
•
todos los se
[¡ : z ,
= z + si →
Re , , , =3
,,
Imlz ) ,
=
5 =
•
•
Si la
parte imaginario es 0 ,
éste se reduce a -
un número real
Ej : Zz =
-
5
•
Si la
parte real es 0 ,
éste se dice que es
un número imaginario puro .
Ej : 2
,
= -
asi
Dos números
•
complejos son
conjugados si tienen La misma parte real
y sus
partes imaginarios son apuestas
2-
2 ✗
yi ✗
yi
=
= + → -
Ej : 2
,
=
3- si ; 2
,
= -5 ; 23
=
3i
Dos números complejos son opuestos si tienen Las
partes reales opuestas y Las
partes
imaginarios apuestas también
Z = ✗ +
yi → -2 = x
yi
- -
POTENCIA n - ÉSIMA DE I : i
'
= -1 ,
i
} = -
i ,
¡ 4=1 ,
is =
i , . . .
La potencia n -
ésima de i, i
"
,
es
igual a ir
,
donde r es el resto de La división
de n entre 4.
SUMA Y RESTA
Z,
22
=
=
X,
X
,
+
+
yzi
yei
} Z ,
± 22
= ( ×, ± ✗ 2) + ( y, ±
y 2) i .
MULTIPLICACIÓN ¡ 2=-1
[ ¡ 1. f) ( 11-4 e.) (1+2) =
1 + Zi + Yi + sist =
1-8+2 + ni = -
7- + Gi .
DIVISIÓN :
multiplicamos por conjugado el .
1Gt "
r
2
Ej :( Yi + 2) É =
4 +
=
Si + si -16
=
-12+161
.
. =
1- i a -
i , _
¡ l -
i
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