Question

A rectangle of maximum area is inscribed in the circle $|z-3-4i|=1$. If one vertex of the rectangle is $4+4i$, then another adjacent vertex of this rectangle can be

• A. $2+4i$
• B. $3+5i$
• C. $3+3i$
• D. $3-3i$

Answer 1

Answer: (B), (C)

The correct options are
B $3+5i$
C $3+3i$

A rectangle with constant diagonal length having maximum area is a square.
Since one vertex is $4+4i$, and the center is $3+4i$, then the opposite vertex will be $2+4i$.
The other two vertices of the square will be obtained by rotating $4+4i$ about the center by $\frac{\pi }{2}$ either in clockwise or anti-clockwise direction.
Hence, the points will be $3+3i$ and $3+5i$.