Question

The minimum possible value of
$|z{|}^2+|z-3{|}^2+|z-6i{|}^2(z\in C)$ is

• A. $45$
• B. $15$
• C. $60$
• D. $30$

Answer 1

The correct option is D $30$

The geometric meaning of the expression is the sum of the squares of distances of any point inside $P$ to the vertices of the right angled triangle formed by points $(0,0),(3,0),(0,6)$. The least value of the sum of squares of any point inside the triangle to the vertices turns out to be $30$.