AP EAMCET · Maths · Complex Number
\(A\left(z_1\right)\) and \(B\left(z_2\right)\) are two points in the argand plane. Then, the locus of the complex number \(z\) satisfying \(\arg \left(\frac{z-z_1}{z-z_2}\right)=0\) or \(\pi\), is
- A the circle with \(\overline{A B}\) as a diameter
- B the ellipse with \(A, B\) as extremities of the major axis
- C the perpendicular bisector of \(\overline{A B}\)
- D the straight line passing through the points \(A\) and \(B\)
Answer & Solution
Correct Answer
(D) the straight line passing through the points \(A\) and \(B\)
Step-by-step Solution
Detailed explanation
Let the point \(z(x, y), z_1\left(x_1, y_1\right)\) and \(z_2\left(x_2, y_2\right)\). \(\begin{aligned} & \therefore \quad z-z_1=x+i y-x_1-i y_1 \\ & =x-x_1+i\left(y-y_1\right) \\ & \text {and } \quad z-z_2=x+i y-x_2-i y_2 \\ & =x-x_2+i\left(y-y_2\right) \end{aligned}\) Now,…
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