Syllabus Question (1 Viewer)

[NubMuncher]

HSC 1987 Q4 iii

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 ans iz respectively. Find the complex number represented by B.

b) The square is now rotated about O through 45 degrees in an anticlockwise direction to OA'B'C'. Find the complex numbers represented by the points A', B' and C'.

I can do this question using vector addition but i believe its under the geometric representation of complex numbers.

Any help appreciated : )

 

[ohexploitable]

a)
AB=OC

OB=OA+AB
OB=OA+OC
OB=z+iz
OB=z(1+i)

 

[ohexploitable]

I can do this question using vector addition but i believe its under the geometric representation of complex numbers.

Didn't see this...

I'm pretty sure vector addition is a part of geometrical applications.

 

[ohexploitable]

b)
A'=zcis45
B'=z(1+i)cis45
C'=zcis135

 

[NubMuncher]

Yeah that's pretty much how i did it.
Thanks though : )