Page 171 - Math Grade 11 (Advance)

PROEUS DARA

o , o ( 1 + i) 2n "' 0 ell ., ~
ruUTifif!ll 2 ?Hl.flSl z = - -. tt:1ru n dltHHlf:'ifi~9fl9ti~r:l'i:fl£ '1
.. 1 -l IJ 1 i.J' 1:3-
GtYW tf:'iQl£ l+i = (l+i)(l+i)- 1+2i-l = i
1 - i (1 - i)(l + i) - 1 + 1
Gil
tuHtuHi~s~2u i dl9tytlL~tfflrul'HlUi

i 'Hl£ a = 0 2b b = 1 tf:'iQlf:l r = J()2;i2 =

, ..n ·~~ a 0 £w smcp =- = 1 t'Ulfi&£g cp =- '1
:rt
b
"' J..t
•WILU coscp =- =
•
r r 1 2
i = cos~+ isin~ '1
2 2
• 2n ( :rt .. :rt)2n
z = (1) = cos + 1sm
2 2
= cos( 2n x ID + isin( 2n x ~)
= cos(n:rt) + isin(n:rt)

= (cos:rt+isin:rt)n
n ..,
""
z = (-1) '1 m n ~ ' z = t'UliDtti
"" n Ctutu z = -1

l+sincp+icoscp)n [(:rt )] ··[(:rt )]
1
( 1 + sin cp - i cos cp = cos n 2 - cp . + sm n 2 - cp
1 + sincp + icoscp _ ( 1 + sincp + icoscp)( 1 + sincp + icoscp)
I + sincp- icoscp - ( 1 + sincp- icoscp )(1 + sincp + icoscp)
' 2
_ (1+sincp+icoscp)
2
- (1 + sincp) - (icoscp) 2
2 2
= 1 + sin cp- cos cp + 2sincp + 2icoscp + 2isincpcoscp
. . 2 2
+
1 2 sm cp + sm cp + cos cp
t <-h ·~~ • 2 1 2
• w 1 LU sm cp = - cos cp
2
_ 2sin cp + 2sincp + 2icoscp + 2isincpcoscp
- 2(1 + sincp)

_ 2sincp(l + sincp) + 2icoscp(l + sincp)
- 2(l+sincp)
_ (1 + sincp)(2sincp + 2icoscp)
- 2(1 + sincp)
= sincp + icoscp

, !:11 ru sin cp = cos G - cp) 2 t~ cos cp = sinG - cp)

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