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martins
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#1
Report Thread starter 16 years ago
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In an argand diagram the point A has coordinates (1,0) and the point B has coordinates(0,2). The point P represents the complex number Z. Given that arg[(z-1)/(z-2i)]=pi/4 describe the locus of P and show that the point (1,3) lies on this locus.
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SsEe
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Report 16 years ago
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arg[(z-1)/(z-2i)] = pi/4
arg(z-1) - arg[(z-2i) = pi/4
By considering what this means geometrically and remembering circle theorems from year 11 or whenever you'll see it's the arc of a circle passing through A and B. Call P a point on the arc. Angle APB = pi/4.

Sub z=1+3i into arg[(z-1)/(z-2i)] and see if it's pi/4.
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