2 c e x e r c is e 2 . 7 h i h d ifi d f th i h g pl + 3i b 2 a...b g iv en that garg (w u) = a r w...
TRANSCRIPT
由 扫描全能王 扫描创建
气v a lu e o f l2
?- z w l.
S h o w th a t lz - w l = 1 + 43 a n d h e n c e fin d th e e x a c t
1 Iźwı ii
b H e n c e fin d th e e x a c t v a lu e o f
a F in d th e e x a c t v a lu e s o f lz l a n d Iw l.
4 z = 1 + i a n d w = 1 - iJŔ
G iv e e x a c t a n s w e r s w h e r e a p p r o p r ia te .
3 C o p y an d c o m p le te th e fo llo w in g ta b le .
a s s u m e d to b e in ra d ia n s .
A n g le s w h ic h inv o lv e n a re
fo r ra d ia n s .
Th e s y m b o l'
s t a n d s
a c e s .
d v w h e r e lv ı = Jio a n d a rg v = -
T ĺ
12c w h e re ıu t = 1 . 5 a n d a r g u = E
b w , w h e re lw ı = 6 a n d a r g w =- 2 . 8 c
a w h e r e ız l = 3 a n d a r g z = 1 . 5 6
G iv e r e al a n d im a g in a r y p a r ts o f e a c h n u m b e r to tw o d e c im a l p la
E x ) r e s s e a ch n u m b e r in c a r te s ia n fo r m .
e z - J2 + 3i f z - ĺ _
c z = - į + į i d z = - 2 - 4 i
a z = l + 3 i b z = 2 - 5 i
a r \ m e n t to tw o d e c im a l p la c e s .
In e a c h c a s e giv e th e m o d u lu s in s im p lifie d s u rd fo r m a n d th e1 E x ) r e s s th e s e c o m p le x n u m b e r s in m o d u lu s - a r g u m e n t fo r m .
E x e r c is e 2 . 7
2 C o m p le x n u m b e r e
盤
由 扫描全能王 扫描创建
4 5
a w , giv e n th a t lz w l = a n d a r g (w ) = - l1T
c a r te s ia n fo r m ,
9 F o r z = 1 + , u s e th e in fo r m a tio n giv e n t o fin d , in e x a c t
d F in d th e a r e a o f tr ia n g le o A B a n d h e n c e s h o w th a t s in B ó A = ·
1
r e p r e s e n tin g th e n u m b e r s z a n d w re s p e c tiv e ly .
c Illu st r a te , o n a s in g le A r g a n d d ia g r a m , th e p o in ts A a n d B
ta n- '
l l)" "- '
l l)b G iv e n th a t a r g (w u ) = a r g w + a r g u , fin d th e e x a c t v a lu e o f
a S h o w th a t lz w l = lu l a n d fin d th e v a lu e o f
z · l + i, w . 2 + i a n d u = 3 + i
c H e n c e , o r o th e r w is e , fin d th e v a lu e o f Iz + w l.
b Illu str a te , o n a s in gle A r
g a n d d ia g ra m , th e c o m p le x n u m b e r s z a n d w .
m o d u lu s - a r \ m e n t fo r m .
a s h o w th a t b = - 44 3 a n d h e n c e e x ) r e s s w in e x a c t
It is g iv e n th a t Iz M l = 16
7 z = ì(. " (Ŝ . + i s in (ĝ 1r)) °n d w = 4 + b i w h e r e b < o .
c H e n c e , o r o th e r w is e , e x ) r e s s z in m o d u lu s - a r g u m e n t fo r m .
b E x p r e s s z in e x a c t c a r te s ia n fo r m .
fo r m fo r z
a B r ie fly e x ) la in w h y th is e x ) r e s s io n is n o t th e m o d u ıu s - a r g u m e n t
6 z = J3(. " (į 1r)- is in (ĝ · ))
ii c a r te s ia n fo r m .
m o d u lu s - a r g u m e n t fo r m ,
b G iv e n fu rth e r th a t a rg w
= - llr , e x ) r e s s w in4
2 C o m p le x n u m b e r e
a S h o w th a t lw ï - lJ 2
c o m ple x n u m b e r .
b It is g iv e n th a t z - 3 + 43 i a n d í = 246 fo r w a p a rti c u la r
由 扫描全能王 扫描创建
4 6
to tw o d e c im a l p la c e s .
n c a lc u la te t h e d is ta n c e A C g iv in g y o u r a n s w e r c o r r e c t
fin d th e a r e a o f t r ia n g le O B C
c H e n c e
b G iv e n th a t a q g ) = a rg w - a rg z , s h o w th a t a n g le c o B = ŕ1r
a E x ) r e s s z a n d w in m o d u lu s - a r g u m e n t fo r m .
p o in t c r e p r e s e n ts .
c o m p le x n u m b e r s z = J + i a n d w = (- 1 + i) r e sp e c tiv le ly .
1 2 P o in ts A a n d B o n th e A r g a n d d ia g r a m r e p r e s e n t th e
q u a d r ila te r a l O A C B .
12b G iv e n th a t a
r 8 (z w ) = į 1r , fin d th e e x a đ a r e a o f
a F in d th e e x a c t v a lu e o f ız w l.
p o in t C re p re se n ts z w .
c o m p le x n u m b e rs z = 1 + 43 i a n d w = 2 - 2 i re sp e c tiv ely .
1 1 In th e A r g a n d d ia g r a m , p o in ts A a n d B r ep r e s e n t th e
d l u - 11· 뉘
a lz w - z l b ız + z w l
1 0 G iv e n th a t lz l = 3 a n d w - 1 + 2 4 fin d th e e x a c t v a lu e o f
2 C o m p le x n u m b e r s
由 扫描全能王 扫描创建
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