Complex numbers (1 Viewer)

[samuelclarke]

Plot points 2i, (root3) - i and (-root3) - i on argand diagram. prove that P, Q and R respectively are the vertices of an equilateral triangle.

 

[umm what]

find distances PQ, QR and PR, they should be equal.

 

[karnbmx]

find distances PQ, QR and PR, they should be equal.

better still, use arguments to find the angles of the triangle, and prove that they are equal.

 

[Carrotsticks]

better still, use arguments to find the angles of the triangle, and prove that they are equal.

Better still, show that:



For the 'If and only if case' but since we only want to show one side of the 'iff', we can just show:



And we can clearly see with the 3 vertices there that it is the case.

 

[umm what]

I don't get it :S

Better still, show that:



For the 'If and only if case' but since we only want to show one side of the 'iff', we can just show:



And we can clearly see with the 3 vertices there that it is the case.

 

[Carrotsticks]

I don't get it :S

It's a very well known 'property' of complex numbers.

 

[umm what]

Better still, show that:



For the 'If and only if case' but since we only want to show one side of the 'iff', we can just show:



And we can clearly see with the 3 vertices there that it is the case.

I don't get the second step

 

[karnbmx]

Better still, show that:



For the 'If and only if case' but since we only want to show one side of the 'iff', we can just show:



And we can clearly see with the 3 vertices there that it is the case.

Is this even within the scope of the HSC???

 

[RealiseNothing]

Is this even within the scope of the HSC???

If you treat them as vectors, they end up back at the origin. Hence: