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Question

locate the points representing the complex number z for which
arg(z1iz2)=π3

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Solution

We know from Cor P.71 that
arg(zz1zz2)=α represents a circle whose chord AB joining the point z1 and z2 subtends an angle α at the circumference. Hence the equation represents a circle whose equation can be shown to be
3(x2+y2)(331)x(31)y+232=0
tan1y1x1tan1yx2=π3 etc.

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