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Argand plane and polar representation - class-XII
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If $z _{1}=8 +4i,\ z _{2}=6+4i$ and $arg \left(\dfrac {z-z _{1}}{z-z _{2}}\right)=\dfrac {\pi}{4}$, then $z$ satisfy
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A
$|z-7-4i|=1$
💡 Explanation:
The equation arg((z-z1)/(z-z2)) = pi/4 represents an arc of a circle passing through z1 and z2. Given z1=8+4i and z2=6+4i, the midpoint is 7+4i. The geometry of the angle pi/4 implies a specific circle equation.