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About LinkBacksOn an Argand diagram, the points P and Q represent z1 and z2 respectively. OPQ is an equilateral triangle. Show that z1² + z2² = z1z2
Since the sides of an equlateral triangle all have the same length sides we know:Originally Posted by acevipa
|z1|=|z2|=|z1-z2|
The internal angles of the triangle are all 60 degress so we also know:
arg(z1) = arg(z2) + 60
And
And
arg(z1^2)=arg(z2^2) + 120
So if z1=then z2=
and
=r^2(1\angle2\theta+1\angle( 2\theta+120))=r^2(-1\angle(2\theta-120)))
)=r\angle\theta(r\angle(\t heta+60))=z1z2)
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