Question

A rectangle of maximum area is inscribed in the circle $|z-3-4i|=1$. If one vertex of the rectangle of 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 $3+3i$
C $3+5i$

Clearly, the rectangle with maximum area is a square.

Let the adjacent vertex be $z.$
Then,
$\frac{3+4i-\left(z\right)}{(3+4i)-(4+4i)}=e^{\pm i\pi /2}$
(by rotation about center)
$\Rightarrow 3+4i-z=\pm i(-1)$
$\Rightarrow z=3+4i\pm i=3+5i$ or $3+3i$