noobie complex numbers (1 Viewer)

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hehe

umm..quite stuck on this 2question

Find complex numbers z and w such that
|z| = 1, |w| = 1 and z + w + 1 = 0

and

given that z and w are complex numbers, prove algebraically that
|z + w|² + |z - w|² = 2|z|² + 2|w|²

hmm..i assume the geometrical interpretion is that it is a locus??

 

[Rorix]

let z=a+bi, w=c+di

you should be able to take it from there

 

[ngai]

lol rorix
not feeling kind today?..eng speech getting u angry?

first question:
draw ur unit circle
put z somewhere
draw in -1
then, w = -1 -z
so join up -1 and z to get ur w
and u want that length to be 1
so clearly, u need the pts z, w, -1 to be an equilateral triangle
hence (w,z) = (cis120, cis-120)

2nd question:
use the rule: |A|^2 = A*(A bar) for all the |something|^2
expand and conquer

also, u can use z=a+bi, w=c+di too...try and see how it goes

"hmm..i assume the geometrical interpretion is that it is a locus??"
geometrical interpretation...of what?
of the 2nd question?
if thats wat u meant, then no it is not a locus, it is a geometry result of a parm