\( P(z) \) is the point moving in the Argands plane satisfying arg \( (z-1)-\arg (z+i)=\pi \) th... VIDEO
\( P(z) \) is the point moving in the Argands plane satisfying arg \( (z-1)-\arg (z+i)=\pi \) then, \( P \) is
(a) a real number, hence lies on the real axis.
(b) an imaginary number, hence lies on the imaginary axis.
(c) a point on the hypotenuse of the right angled triangle \( O A B \) formed by \( O \equiv(0,0) ; A \equiv(1,0) ; B \equiv(0,-1) \).
(d) a point on an arc of the circle passing through \( A \equiv(1,0) \); \( B \equiv(0,-1) \).
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