Question

If 'z' be any complex number such that |3z - 2| + |3z + 2| = 4, then locus of 'z' is:

• A. A circle
• B. An ellipse
• C. A line segment
• D. None of these

Answer 1

The correct option is C

A line segment

|3z - 2|+|3z + 2| = 4 $\Rightarrow$ |z - $\frac{2}{3}$| + |z + $\frac{2}{3}$| = $\frac{4}{3}$. If z be the point P,($\frac{2}{3},0$) = A,($\frac{2}{3},0$) = B, then we have PA+PB = AB. Thus p(z) is any point on the line segment AB.