Page 160 - Math Grade 11 (Advance)

PROEUS DARA

'11jltlt9J61 ZIZz =(I +i)(l +iJ3)

= l+iJ3+i-J3

= l-J3+i(I+J3) (2)

tLu]mcrJu (1) sh (2) tmflufll[!JOlS

7 7 1
2Jicos rt = 1- J3 ==>cos rt = - J3 = Ji- ./6
12 12 2Ji 4
7
7
2Jisin rt = 1 + J3 ==> sin rt = + J3 = Ji + ./6
1
12 12 2Ji 4
7 7
cos rt = Ji - ./6 S h sin rt = J2 + ./6 '1
12 4 12 4

1
~5iei 2 t?'i'HlS ZI = 6(cos~~+isin~~) Stl z 2 = 2(cos ~+isin~) '1 ?'iru"JSl

ZIZz ~tHuHM~ctl9~ci a+ bi '1

Mth6'1USSRGumnHsussrH~u z ttl z = r(cos<p + isincp)
n 1.1 1w "" 1.1 1ov
= (rcos<p) + i(rsin<p)

C?'iQlS z = (rcos<p)-i(rsin<p) = rcos(-<p)+i[rsin(-<p)]

os . ...,
0 c::ll
tWtSll uSSrhsuffihltS z = r(cos<p+isincp) ?1 z = r[cos(-<p)+isin(-<p)] '1
u 1.1 l6V 6V

z z 1 z ri(cos<p + isin<p ) r [cos(-cp ) + isin(-<p )]
- = - X = = 1 1 X ---:---:----:---:--:----,-:::
2
2
2
1
2
z z r (cos<p +isincp ) r [cos(-<p )+isin(-<p )]
2 2 22 2 2 2 2 2 2
2
r I r [ cos cp I cos ( -<p ) + i cos<p I sin ( -<p ) + i sin cp I cos ( -<p ) + i sin <pI sin ( -cp )]
2
2
2
2
2
=
?
r r [ cos<p cos ( -cp ) + icos<p sin( -cp ) + i sincp cos( -<p ) + r sin<p sin( -cp )]
2 2
2
2
2
2
2
2
2
2
r I [cos cp cos ( -cp ) - sin <p sin ( -cp ) + i( cos cp sin ( -cp ) + sin cp cos ( -<p ))]
2
2
1
1
1
2
2
1
= ~-~---:--~-~~~~~~--~~~~--:-~-....,-~~
r [ cos cp cos ( -cp ) - sin cp sin ( -cp ) + i( cos cp sin ( -cp ) + sin cp cos ( -cp ))]
2
2
2
2
2
2
2
2
2
r (cos0 + isinO)
2
= ~[cos( cp - <p ) + isin( cp - cp )]
2
1
1
2
rz
155