what does this locus mean:
$$\Re\left(\frac{z-z_1}{z-z_2}\right)=0$$ I know it is a circle but can anyone tell a geometric approach, just by looking at the equation ?
2026-03-26 22:13:14.1774563194
Meaning of a locus.
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It means $\;\DeclareMathOperator{\arg}{arg} \bigl\lvert\arg(z-z_1) -\arg(z-z_2)\bigr\rvert=\dfrac\pi2$.
Geometrically, if $M, M_1, M_2$ are the affixes of $z, z_1, z_2$, the geometric angle $\; \widehat{M_1MM_2}$ is a right angle. Hence the locus is the circle with diameter $M_1M_2$, deprived from $M_1$ and $M_2$.