AP EAMCET · Maths · Complex Number

Let $A (3 - i), B (2 + i)$ be two points in the Argand plane. If the point $P$ represents the complex number $z = x + i y,$ which satisfies $|z - 3 + i| = |z - 2 - i|,$ then the locus of the point $P$ is

A the circle with $A B$ as diameter
B the line passing through $A$ and $B$
C the perpendicular bisector of $A B$
D the ellipse with $A B$ as major axis

Verified Solution

Answer & Solution

Correct Answer

(C) the perpendicular bisector of $A B$

Step-by-step Solution

Detailed explanation

Given, A3-i⇒A≡3,-1 B2+i⇒B≡2,1 Now, z-3+i=z-2-i ⇒z-3-i=z-2+i≡z-A=z-B ⇒z-3-i=z-2+i≡P-A=P-B Therefore, we get AP=BP. Point P is moving along the line CM such that AP=BP. Hence, locus of the point P is the perpendicular bisector of…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Let A3-i,B2+i be two points in the Argand plane. If the point P represents the complex number z=x+iy, which satisfies z-3+i=z-2-i, then the locus of the point P is

Step-by-step Solution

Let $A (3 - i), B (2 + i)$ be two points in the Argand plane. If the point $P$ represents the complex number $z = x + i y,$ which satisfies $|z - 3 + i| = |z - 2 - i|,$ then the locus of the point $P$ is