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#1 2008-12-05 21:21:26
- GemmaJ1988
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- Registered: 2008-10-08
- Posts: 39
complex plane
show that the points
lay on the same line in the complex plane if and only if
does anyone know how i would go about solving this?
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#2 2008-12-06 03:37:05
- Kurre
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- Registered: 2006-07-18
- Posts: 280
Re: complex plane
uhm what the hell is x?`??+
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#3 2008-12-08 12:18:57
- mathsmypassion
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- Registered: 2008-12-01
- Posts: 33
Re: complex plane
x is a real number probably
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#4 2008-12-08 12:29:59
- mathsmypassion
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- Registered: 2008-12-01
- Posts: 33
Re: complex plane
We actually have two problems here, because of if and only if.
First you need to prove that if z1, z2, and z3 lay on the same line then that fraction is a real number. Secondly you have to prove that if the relation is right then A,B and C are collinear points.
Use coordinate geometry after you alocate for z1 a point, let's say A(x1,y1), for z2 a point B(x2,y2) and for z3 a point C(x3,y3).You will discover, after you multiply the fraction with the conjugate expression, that the numerator is nothing else then a necessary and sufficient condition for collinear points.
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