Search any question & find its solution
Question:
Answered & Verified by Expert
$A\left(z_1=2+2 i\right), B\left(z_2\right), C\left(z_3\right)$ are three points on the Argand plane satisfying $\left|z_k-2 i\right|=2,(k=1,2,3)$. If $\triangle A B C$ encloses the maximum area, then the sum of the imaginary parts of $z_2$ and $z_3$ is
Options:
Solution:
1225 Upvotes
Verified Answer
The correct answer is:
4
According to given information $|z-2 i|=2$ is a circle having centre is $(0,2)$ and radius is 2 .
If the area of $\triangle A B C$ is maximum the triangle must be equilateral triangle and point $M$ is the mid point of $B C$, where $M$ is the foot of perpendicular of point $A\left(z_1=2+2 i\right)$ on $B C$.
$\therefore$ Sum of the imaginary parts of $z_2$ and $z_3$ is twice of the imaginary part of $M=2 \times 2=4$.
If the area of $\triangle A B C$ is maximum the triangle must be equilateral triangle and point $M$ is the mid point of $B C$, where $M$ is the foot of perpendicular of point $A\left(z_1=2+2 i\right)$ on $B C$.
$\therefore$ Sum of the imaginary parts of $z_2$ and $z_3$ is twice of the imaginary part of $M=2 \times 2=4$.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.