complex no. questions (1 Viewer)

leisl1990

Member
Joined
Feb 13, 2007
Messages
108
Gender
Male
HSC
2008
(a) Let OABC be a square on an Argand diagram where O is the origin. The points A

and C represent the complex numbers z and iz respectively. Find the complex
number represented by B.
(b) The square is now rotated about O through 45° in an anticlockwise direction to
OA'B'C'
. Find the complex numbers represented by the points A', B' and C'.

They are from the 4unit syllabus..

 

Trebla

Administrator
Administrator
Joined
Feb 16, 2005
Messages
8,114
Gender
Male
HSC
2006
(a) NB: the bold font represents vector notation
OB = OA + OC
.: B = z + iz

(b) OA' = cis π/4 x OA
.: A' = z(1 / √2 + i / √2)

OB' = cis π/4 x OB
.: B' = cis π/4 x (z + iz)
= z(cis π/4)(1 + i)
= z√2(cis π/4)²
= z√2(cis π/2) by DeMoivre's theorem
= iz√2

OC' = cis π/4 x OC
.: C' = cis π/4 x (iz)
= iz(1 / √2 + i / √2)
= z(- 1 / √2 + i / √2)
 

leisl1990

Member
Joined
Feb 13, 2007
Messages
108
Gender
Male
HSC
2008
Trebla said:
(a) NB: the bold font represents vector notation
OB = OA + OC
.: B = z + iz

(b) OA' = cis π/4 x OA
.: A' = z(1 / √2 + i / √2)

OB' = cis π/4 x OB
.: B' = cis π/4 x (z + iz)
= z(cis π/4)(1 + i)
= z√2(cis π/4)²
= z√2(cis π/2) by DeMoivre's theorem
= iz√2

OC' = cis π/4 x OC
.: C' = cis π/4 x (iz)
= iz(1 / √2 + i / √2)
= z(- 1 / √2 + i / √2)
thanks very mch
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top