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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

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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

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Ș. kl'

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