Summary
Summary Complex Numbers
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Handwritten cheat sheet for Complex Numbers by JEE 2020, GATE, and CSIR topper.
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atharvashinde
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Complax"AA no. of he fosmn X+ ly,where KyéR &i:
is calleda complex na.
Na = al
i"= j49rr-i99,i)': j
n t3
Recz)=x Iney
Acomples no. s purelyrel if Lm(z) =6_&
paely
Acomplexnaginang
ho. ia an imaginany no. dt and
and
"||A
Inlz) t0 only if
LAJL no. except Oae Im na, but
an Im. Vno.inaghay
"maox may not be pualy Ena
RCC
let z=Q+b & Z =Ctid
212, = (ac -bd)+ jCad tbe)
Z2
ZL - actbd
c'+d?
iChc ad
c²+d2
Addiive inuexse of z is -z
Complex no. do not passes he praperty of
af ader
i.e is not dehked
, is"
conjugate oF Conjugate la'tb²|
lzl= Na-ibNatib (xtis)´)
atib=
firpertiegofGeometically,2 F a+ib: atib2=Sq.
2=atib xoot
in
+
the 2
of
ofLV2J S.T
eal hen a
lzlta 2 2
imngiot he a 2 complex
as its -izl-aIz+o
l2
Complax
conjugate canjugate to&
+i|e-a
is no.
2
2i 2
kiy
2
Pez) ofz is
is~eQ-ib fox 2
the b>Q
eletion
,
"lZ+':
ll'tz "-lzl< 1JF
*Modulug
lzl"lz" = Zzl= Fropexties
Mooulug of Gesmenically
axb=-Nab ZZ,'= 1zlO atbthenZ= conugate
zl=l
Relz)<lz
l2.llz.l then then
(2tz) ofa of
b<O a,
if z Jz=
n is 22 PCz)
Complex
(72,) genesal &-zl< is
is
kncutn
knocotn
knetat -i7
_lZZ2,.= ZOP
= as no.
lzftlz.t lm as
(z)< unimodular
O
lzl modular
zllzllz,..
G2+~.2) cemplex
complex
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