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Class notes

Algebra and analytical geometry class notes

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Class notes for the entire course. Passed with 6/10

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2- 11-3 i
Conjugado
=




real 12-1=12+32

parte igual
Racionales '
12-1=1+9
oparre imaginaría opuesta
o I 12-1=10

=/ Es , a. b.cz ,
b. Reales ≠
complejos

◦ 2+ > ¡ → z .



imaginarios !

IZ / = cítb




]
Irracionales

2=1+3
inlzn
m.aaa.mag.name w = -4 -
Zi

eje imaginario E = -1 ✓ = 2- Si
n
Forma binouica
pspiragoras!
t
- -- - •
A

b. . . . . . . .




i
Z 2- =


#Li

ayb son reales i
i
fstongitursosuódulo 2- zo


i
real
img ¡
→ Angulo
> Vector

Argumento
-





¡
r
PAR Gvmenoo
◦ ≤ D- < 21T
' ,
)
i . Retz)
i
> ! i
a ese real
¿
× y
1. ¡ i
haha )
=
◦ + ÷ . . . . . . . - - -



l



(E)
W
'
:
Zi ◦ + 2. i ⊖
g-
-

_

- - - - - - - •

r
b
-
bi = o -
3. i a #o
n


Forma exponencial forma trigonométrica ,



2- Íp .
- ir
45º
>
r

2- = atbi
d
< COJ ⊖ =
=
§ → a
=p . nos ⊖ ver tí




.ws/o)tp.senfoI.isenO------bp-
IWI = 2


2- =p →
b =P .
Seno '
(f) 45º -
[
g- =




2-
=p [costó 1- i. Sento)
.
Mig .
• WEE [ nos /%,) +
.
i. sen /%)
-
rz.ci
.




Formula de Euler exp . • W =

, radicación
r

zkijfw.ei.ws
"" "
◦ ≤ v. ≤ n -1 KEÍ
no
,

"
2-
\
= w




ZK F. [ nos /% -_
"' "
n
+ ¡ .sn/YrwltkE)) n
= -
1 Potencias
1




z3-4i-4.jp
Ii? -2 ¡=L 4

{j1 train > cuadradas de -2 ¿
"
= i
3
9 .

rodeen
:
"




¡
z ¡ ¡

¡
.
= -




n_
-
4. qtr
"
¡ =L
NE
FEI 532 __
¡ = i
[ g-
« e' ".




ej
'
Í ,
=
0,790¥, ¡

= -2 Ej
+ '"
¡ = -
¡ ¡ = ¡0=2

✓ "
raíces ubicas de 41-4 i : '
¿
.


= ¡ =L


¡
"

2- =p .é° 5. = 5. i? -
5
% + 2. k.it


tu # ¿ ftp.eioY
'




=
3 K 0.1.2
-
-

[=
/ E) i r .az/z)
.




¿ →%

"
2- =
% + 2.0.x

¿
'




% " ]
2- =
3

12-7=12-1
"

.


" " "" '




⇐¿ / Itai ) Eres ?
.

Ejl
2- i-F.ci V32 ( EH sentir]
""
.




[ no> + i. Util


.ir#u=y..j:ik=jtfi-E
.



" "

V32 /0,7 + i. 0.71=11,251-1,25 µ.
"
f. µ
?
. •




2-2=532 ei 1,253+3.1 .rs?1,rsit- 3. 1,23 1,2%+1,23? / MTIÍ )
"




54.org/rti)--54.yI--2=-nT.EoslYE7+i.sen/EH
=
arg
.

. •




} 1,95+4,7 .
-
4,7 -1,95 .
i




Operaciones de complejos
ej.tn

I.
a

2- = -53 ti

12-1=-55+12--2


( 30º -561T
" ✓
O = [
g- → - →
ISÓ → Suma multiplicación División


sentar)]
2- =
/¡ it) + E- E. E-
2- = 2. [ nos i. • a +
/ az b
,
+
bz •

IWIZ
?""
2. e b bz " El:| EJL ( 3- Gititz) 5- Si I
§ §
2- + tsti
.
= a 1- 2a
Éi Éi =/
1
az 3. te
- -
-
• • •
, , = = = -
¡ =

Ji
-



ntzi 1-ziti + 4) 5
Z -31-4 i
ej
=
• .
,



L
2-2=5 -
Gi observación !


multiplicación con reales (-3+5)/4+1 - -
-
6) )
i w.IE> unir


f- Z f. (-31-4)=-23-+2
}
i Zi
,
-
_

7,1-2-2--2 -

w
-
_ atbi
/atbil.la bi -




=

Z
, -2-2=-8+10 i Ñ=a -
bi a2-abxtab-i-fb.LY
b? -1
lwl? cítb
{¿ 1 : {j 3
7=-3+2 i. w = 5+7 : Ejz
i
zi-4i-htz.tt/s+zi).h-3i)-,f.-=-I-i SÍÉ Í
I

(→ / Sttil Í fi ✓
- -




) = =
. - - -


+ Li
. iii. i. ¡ +
2

-
15 -
Zlitloi -14 ( Yi -
1- 2) ( 5- 15 itzi -16)
+




-29 -
ni ✓ f- l -
Zi) t / 11 -
isi ) {J "
si 3L Iti
=
3in -3
¡÷
-

2- = -

{ Ei ✓ +


= '




1- i ni mi ¡+
Iii
_


lo -




"

EJS frosti)

}
27

tfrsti) /
27 "' "
"
=
153%1=2--2 ¿7. ¿
arglhtst 27.org/Bti)=27./rj'F3)-- 14,1
"
=
2 .
[ nos /14 ,
1) ti .hn/i4,H]
O 2

/ otil
"
2


0+22?






?⃝

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Uploaded on
July 15, 2022
Number of pages
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Written in
2021/2022
Type
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Professor(s)
Virginia bravo
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