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The document contains various mathematical expressions and equations related to complex numbers, including operations such as addition, multiplication, and simplification. It also discusses properties of complex numbers and provides examples of calculations involving real and imaginary components. Additionally, it includes references to algebraic identities and transformations.
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=(2+3i)+(7-2i)=2+3i+ 7-21 = 9+1i=94i
(ii) 26 + 41) —3(7+4i)
2(5+4i)—3(7+4i)= 10 + 8/21 —12/=-11-47
(iii) — 345) - (44+ 91)
—(-3+5i)-(4+9i) =3-Si-4-91=-1-14i
(iv) 2? + 68 + 3/16 — 67! + 45
= 2? + 67? 1+ 3 (P)8-6(2) 1+ 4 (P24
=2(-1)+6(-1)i+3(-1)' -6(-1) i+4(-1)"i
2-61 +3(+1)-6(-1)i+4(I)i
-2-61+34+ 61+ 4i
=3-2+6i-61+4i
=144i
mB @&2 a &
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UPFEPS a + vite 3
(i) (743i) (3+ 20. J
(-7+3i)(-3+2i) =(-7)(-3)+(-7)(2i) +(3i) (-3) + (3i)(2i)
=21-141-91+6i*
=21-231+6(-1)
=21-23i-6
=15-23i Laie f a-v¥-4)G-Vv-4)
b-V)(0-3)
(2-2i)(3-2i)
=(2)(3)+(2)(-2i)+(-2)(8)+-2)(-21)
=6-4i-6i+4i?
= 6-10i+4(-1)
=6-10i-4
=2-10i
ii) (V5-3i)°
(si) =(v5)' -2(v5)(a4)+(30)
=5-6Y5i+9(-1)
=5-6y5i-9
=-4-6V5i
in) @-3) B= 2/)
(2-3i)(3=2i) = (2-3i)(3+2i)
=(2)( oe
=6+4i-
Se aaa)
=6-Si+6
=12-Si
92
Ly bei =20i) 242
Ti TH Ti Gtp)-) (1? -GP
242i _-2+2i _-2+2i
2
)(3)+(-3i)2i)
AAP Sa + bio 4
ww 243) _ 2431, a4i _ (2+3/)(44i)
4-7 4-i (4-A (441)
(2)(4)+(2)()+ “GCN, aszisiotey
(4 -(i" 16-(-1)
—8+l4i+3(-l) 4147-3 _ 54141
16+1 AT 17
ay ii
1717"
9-7
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9-71 _9-Ti, 3-1 _(9-7)(3-i) _ (9)(3)+(9)(-1) + (-71)(3)
347 S48 “3-7 B+GB=1) (3) -(i
20-301 _ 20. 30,_
F109 10 10,
©) Ss
2-61 4+i — (2-6i)- (4+i) _ 2-61-4~i_ =22-7i ~2-7i 3-i
341 341 3+i 3+i 34 SH 3a
GHG By -(@?
= 26-191-7 _-13-191 13 19,
941 10 10 10°
1+iy
(vy) (#4)
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i “Cais imi 4p SZ 4-31 _ 4-37, 2-47 _ (4-3i)(2-4/)
244) 244i 2-41 (2+4i)(2-47)
8-161-61+12i? _8~22i+12(-1) _~4-22i_-4-221 4 20,
(2) -(4iy" 4-167 AAG 200.220 20 73
ya(-b Udy) 21) 1) tt
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on
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25 100 25 100° 100 =—-:100 4
—~ SUSG AI w= 541 i = 243A
@ztwo = +0
LHS. = z+w
ztw = (24+3)+(-4)=24+374+5-41=7-i
zw = J4=7+i (ql)
z+
z 2-3!
w 544i
+54+4=74+7 (2)
Sinente Qa) Aebeut
LH.S.=z-w5
zow = 243i
— (et) (2-3i)-(S+
=iw
aw = (2 +3i) (5 —4i) = 10-8) + 15i- 127
= 10+ 71-121) = 104 714 12= 22+ Ti
pe = 2247 = 22-7
RHS=2Z”
Zz = 243i
w= 5-4
a = 10 + 8i— 15i- 127
2
=z
a
etini = NE
~ 10=23/-12
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w
243:
5-4.
2434, 544i _(23/)(5440)
S-4i 5+4i (5-41)(5+4i)
1048141514127 _ 10+23/+12(-1)
(5) -(4i)° 25+16
10+ 23i-12 _-2423i _-2 , 23,
4. a1 at"
zi.)
=i[N1
+
=5+4i
(2-3i)(5-4i)
544i 544i ° 5-47 “Sa 4i)
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(5) -(4i)" 25-167
EE: i
e ae
I
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na
1
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41
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Ww
we!
a
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FED, eo SAW z
lez 2)=3(2+3i)-(2-3))= Leora 243) =3(6i)=3.«Im(2)
2-39 + yn =44) UM tyson
2-3) +y)=447
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. Ati 2437
xt yi ea
vey (4412431)
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i QF-Giy
ety = SHIQi + 2e 43H?
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é 8414
ey aD
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rey = AS
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ref yall
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3 ~2i) (+ yi) = 2 (x-2yi) + 21-1
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3x + 3yi — 2xi-2y C1 ~4yi)
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> 3xt2y=2x-1 and 3y-2x=2-dy
3x~2x+2y= -1 —2x+3y +4y=2
x+2y= -1 (1) —2x+7y=2 (2) | =
jyen = y= ALIS 2) fel
Ily= y=
x#2(0)= -1 eb ened Sy An rene
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gt 4?-2(-yi)=x+yi
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9+ 247 + 161? — 2x + 2yi= xtyi
g+24i-16 -2x+2yi=x+yi
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(-7-2x) + (244 2y)i=xt yi
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P
a PML ig
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Pedahyg eu fit Toe
R=Qgy = dL
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Be, dea BE Froth Peatoveliger eh 2
MEAs 2 Servier 4
SAE wun Pesieryir bin Sy
EPL Ptegwidit fry ¢
eth Gel Pte
Latta Sul Pasi ipB cll
ple Peseta 2 2 a 0.375 1 = 0.4 pL Jong
SUL Abuser Aird 2
HL LOSI AS Lal Le SER Uses bp DBL 2 vel aE ZN,
UPL US en lee
putbas ua Prsieeya bi? 8
5 sg 4 2
UP MM Peel i WIE EAE 7 = 0363636... hg = 0.222 Ae
5-H
Sen yfo2 F a6
0.23 = 0.232323. i
ut atin inact in 7
vatbeR ech
VabeR ,atbe os pe.
u
4% ounthth byron Gad
atb=b+a.vabeR AY
bia Bek Ss dialects godin cae
Lae Sve S121 E b Sut Pus Sue ise uw. Seeirertiet -17
(a+b) + c= a+ (btc)« VabceR (rea Mele
eonr isi 6 E -18
fret Wid ee sere tisputitnerl inde OK alt
a+0=a=O0+aeVaeR
te bel" Sule -19
S ‘ete 87 aOR GL SAL afin ERIN PS ee
at+(-a)=0=(-a)+a
a “om tb ice coin? 20
abeR, VabeR ieecb rele
yn rabsyoct i? a
ab=ba,VabeR whperbielt
UL i psbpsirecto bun? n
(ab)e=a(be), VabceR pec bee
see Oi POLE -23
Le pe tulardsy pre ra BILE Ree L stale Wle
a.l=a=la-+ VaeR seo ou? 4
(Gh Peak revere! =| 1 A tispo flee 0) se Gen utRer Melt
aat=l=sa7a-o
SY Gb IT eUbh -25
Va.b,ceR » Iz
a(btc) = ab + ac (GH UIE uw
Se Fer YF UL) -26
VabceR wpe
(ath) c= ac + be (HEY IE yuu)
VG Moby Ie Ul 27
Vab,ceR slg
a(b-c) = ab —ac (J Abuds OW :
Se SE Sobuds UW -28
Va,bc eR slg (a-b)c=ac—be CF Sedu se Uw)
SUP YL y 4
“IL x
S a UL v: ‘
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LA SNe OS SUcle hata? 4
a=a VaeR eet,
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UU Aopetbec deta? y
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Lee Mutu?
a=b=>at+c=bte VabceR este
Lect Aton?
a=b=ac=be VWa,bceR weeby rae
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ate=b+c > a=b , VabceR Gebectk ek
Lge Aber Geet? er
ac=be c#0>a=b , WabceR w AbbechF nek
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11
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s
mi
Lae ae ttt nif ebb
et W Ei binesi una Pax A Lite benno tnd xv be
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et SEL,
- fe Ebi KELs a1
ESE LS ase tule Mie LS ont da Uibviglt
te bn P ved 42
EAs SES tied le
ee Pde AS x= Ya PULL x= (ay i
US feck: -43
FJunstelGednmslad ER Ale
4 va =(Ya)” 5. va" =
(*4) Oe, te Uta 44
UE ae BS af mabey "a" Auta’ Pbve de
(216)! x25)}-L™ 45
WEvibtsa
a
z 1 2 a WR
(216)? x (25)? = (2x2%2x3x3x3)) * (5x5)? eh
= Bad OP
wth gthxses
= 22x 3x5
=4x9x5= 180
LASS (5°)* -46
2 ey= st = 5? wee
a?.a>.b’
LPt 5 47
a~b 5
ata’.b’ ath bt ee
7 gt 7 ab
(aloes aAn -48
afi ead DAE Vai wiabe R Ut yrz = at b ie ting
ete le "2" 7
ede bLi 2 = 243i “lz=atbi , al
- 2 sD: cr: 5
Re WL re Pd abi eI at if j me tet)
-etuie
U3 i* 5
MSC =Car,
a.
uA Lite 2-515
2 24S LEE 2 Since
fos HNP Siu 4
Zz ke gh
Re (z) Q
Im(z) =-5
B+4 +743) LAO LPE arbi Sul i bine
(3+4i) + (743i) ad
= B+4i) + (7431)
= (347 + (4443)
= 10477
(245) - Bt) LAP ORI a+ bi sl Be %
(2451) - G4)
2-3) + (5-1
= 544i west
Q-si) (7>3) EPS
(3= Si) (7-31)
= (3~ Si) (7+ 3/)
= (3)(7) — (Si) (34) + (331) + (-51(7)
= 21-157 + 9) - 351
SN = 21-15(-1) + 97-35%
ah PPE a+ bi 58
fi 2-1 el
=i @+N2=i) ~ QF
ne lR
G+3)+0-1i
=6+0i
=6
RF y = ty SEQ y-7-45 wh x=3 4514 00
LHS.=x+y RHS.=X+y, ek
x=3457 x=3+57
Y=7-45 y=7-4i
My = (3451) + (7-41) x=3-5i
= (G47) + (5-4) J=7+4i
My = 1047 X+Y¥=(3-5/) + (7441
y= Tor X+Y= (347) + (544);
BY= 10-1 Xx+Y=10-7
LHS.=RHS,
MY = X+¥ Siete
HOHE
eS
