Q2(d)(i) 2008 Ext2 -- please explain (1 Viewer)

[cssftw]

Can someone please explain Q2(d) (i) i know its pathetic to struggle at such an early question, but this is the first time I've met such an early roadblock.

So why is it, when you do 0.5(Q+R) --> you get M??

thank you

 

[math man]

Think of Q and R as points and M is the midpoint so you average the coordinates

 

[Omnipotence]

Midpoint (2Re(w))

 

[rawrence]

M is the mid point of Q and R so z(w+con[w])/2 and a complex number + it's conjugate = 2Re(w) therefore midpoint is z(2Re(w))/2 = zcos(2pi/3) which can be evaluated as -z/2

And the reason it's 1/2(Q+R) is because like having (x1,y1) (x2,y2) on a cartesian plane, complex numbers represent these on a complex plane in the form of complex numbers x1 + iy1, x2+ iy2, so finding midpoint is simply adding the 2 complex numbers and dividing by 2