COMPLEX NUMBERS
|ROTATION OF (0N PLEX NOS
mt i, im*2-1, im+3 -i,m- |1 As Z2 2l el 0a Toata z thgugh 6.
im4 Mmt mt 3 m
COM PLEX NO. a+ib -22 129-2
REPRESENT ATTUN NO3
MODULUS= vaz+2 =|2l nEohE TRY OF (OMPLEX
ARGUMENT 6 tam (b/a) elon 1gvmulnL
(2,+ ?)/2
PRI MCI PAL
ARGUMENT ¬ (-T/2 , TT/2) Nid povmd f lona ,-2 (2,1
FORM ordo od af D 7, 2 3 2t 2,/3
Cordsonjem (a+ iy) -
to lotaly a Lombla nokl6 Auadulaluhals (2,2, 2 2u
Panalllogum z,+ 3 22 +2y Kobagtnds bisrty
.2Lan atm |Zl (tase+ i sim 6) Uyud whum Rhemus 2 , + 7 2 42y &|Z,-22 = /zu-221
PGuLs is wyhgh, mon and mum&
mhiort of uny Rmalu 2,12g=Z t Z4 lz,-23/ = |23-2sl
3) Eulbr stan |2l
ele e= Lob iiun 0. Sanou )
Zt27+24 &lz,-7)=|a-24|4/z-l=l2-2,|
ALGE RA 3TRAIGMT LINE IN A RhAND PLABE
e
Adcluhon 1,tiy,)+(yt lyz) 0,1)+2(y,+y) =
anby+:0 7,t1y 2
2)Mukpcaton ) 2,2-(74-9.71)+i (,x,t 2, Y2)
(2,2 e*o, *8,) lZ121 Us (6, +0,) a (24) +br4:0
Mulhplrawut imu 2d+ +(=0 rmhvu d:(a+ib) /2
}//212 O E9uaNbn elinu im Argond plov 2d +2d+ (=0
2 Tuo limus au ll = u02 0Ly u+"=0 whu
CONTUATE
- 1y
FuaNon om u 2 tz +(1-Dz,toparomtn
3 E i CECMZ O umgho }gm 2o to
d2 +diio
DE-MOIvRE's THEOREM 2 lT
6 nbisTnb s bro vaus o lwesb isn 6)h Im of 2, wpt a2 ti2tt sofus dz, +2,t{ 0
AUARE Roor COMPLEX NUMBER 7-(2) =-(
CIRCLE IN ARGTAND PLANE
(z= 2h Ss(24T+-8)+isim (20k4|K= 22 whu 2, is tmu, is adus
(-
2 D 2 y 27 +d2 +o7+O
CUBE RDUT OF UNITY
(mtu = d cLclus
isin2ka)ó t a s2Kn, k:a,
e s o im01¥= (w 2Kn Vlc 4
yonduvalus 1,-+i,-ih nuspshuy. 3. Fo psns au ep- ydty 7-2)(2M
Gtu4w=0 Jw.w'sB (2-24)Cz-3)
puruly ral
1+
P a
w"=0,
a uuby
jms mota mulh p t3, se Ualu is3.
robt e a nu. sthw nos au pw d þw IMPOR7AT LOCI
mh nee o undy 2-2 |2-221 L iswon alu /pniny
z, 82
I
. 1 + 4 P n l =z(«)a-Dj tuu I21: 2-2,+ I2-2,l =lz,-2l nu segmunt
(-1)**" I7 ovmg z,822
1.d d .
eoNI' METHO D 2-2, t lzrz,l 12,-2l a ine whvu z
=
3,uv2, 2 4g avu
l ot &n Atgmamd
2,ondl/ J aimng z, 2 7i.
Angh emud uy
m lnua A-: ag2 (2:) = 0 dn, lba'ynt lins
|ROTATION OF (0N PLEX NOS
mt i, im*2-1, im+3 -i,m- |1 As Z2 2l el 0a Toata z thgugh 6.
im4 Mmt mt 3 m
COM PLEX NO. a+ib -22 129-2
REPRESENT ATTUN NO3
MODULUS= vaz+2 =|2l nEohE TRY OF (OMPLEX
ARGUMENT 6 tam (b/a) elon 1gvmulnL
(2,+ ?)/2
PRI MCI PAL
ARGUMENT ¬ (-T/2 , TT/2) Nid povmd f lona ,-2 (2,1
FORM ordo od af D 7, 2 3 2t 2,/3
Cordsonjem (a+ iy) -
to lotaly a Lombla nokl6 Auadulaluhals (2,2, 2 2u
Panalllogum z,+ 3 22 +2y Kobagtnds bisrty
.2Lan atm |Zl (tase+ i sim 6) Uyud whum Rhemus 2 , + 7 2 42y &|Z,-22 = /zu-221
PGuLs is wyhgh, mon and mum&
mhiort of uny Rmalu 2,12g=Z t Z4 lz,-23/ = |23-2sl
3) Eulbr stan |2l
ele e= Lob iiun 0. Sanou )
Zt27+24 &lz,-7)=|a-24|4/z-l=l2-2,|
ALGE RA 3TRAIGMT LINE IN A RhAND PLABE
e
Adcluhon 1,tiy,)+(yt lyz) 0,1)+2(y,+y) =
anby+:0 7,t1y 2
2)Mukpcaton ) 2,2-(74-9.71)+i (,x,t 2, Y2)
(2,2 e*o, *8,) lZ121 Us (6, +0,) a (24) +br4:0
Mulhplrawut imu 2d+ +(=0 rmhvu d:(a+ib) /2
}//212 O E9uaNbn elinu im Argond plov 2d +2d+ (=0
2 Tuo limus au ll = u02 0Ly u+"=0 whu
CONTUATE
- 1y
FuaNon om u 2 tz +(1-Dz,toparomtn
3 E i CECMZ O umgho }gm 2o to
d2 +diio
DE-MOIvRE's THEOREM 2 lT
6 nbisTnb s bro vaus o lwesb isn 6)h Im of 2, wpt a2 ti2tt sofus dz, +2,t{ 0
AUARE Roor COMPLEX NUMBER 7-(2) =-(
CIRCLE IN ARGTAND PLANE
(z= 2h Ss(24T+-8)+isim (20k4|K= 22 whu 2, is tmu, is adus
(-
2 D 2 y 27 +d2 +o7+O
CUBE RDUT OF UNITY
(mtu = d cLclus
isin2ka)ó t a s2Kn, k:a,
e s o im01¥= (w 2Kn Vlc 4
yonduvalus 1,-+i,-ih nuspshuy. 3. Fo psns au ep- ydty 7-2)(2M
Gtu4w=0 Jw.w'sB (2-24)Cz-3)
puruly ral
1+
P a
w"=0,
a uuby
jms mota mulh p t3, se Ualu is3.
robt e a nu. sthw nos au pw d þw IMPOR7AT LOCI
mh nee o undy 2-2 |2-221 L iswon alu /pniny
z, 82
I
. 1 + 4 P n l =z(«)a-Dj tuu I21: 2-2,+ I2-2,l =lz,-2l nu segmunt
(-1)**" I7 ovmg z,822
1.d d .
eoNI' METHO D 2-2, t lzrz,l 12,-2l a ine whvu z
=
3,uv2, 2 4g avu
l ot &n Atgmamd
2,ondl/ J aimng z, 2 7i.
Angh emud uy
m lnua A-: ag2 (2:) = 0 dn, lba'ynt lins
