complex no. questions (1 Viewer)

[leisl1990]

​

(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]

(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]

(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