If the roots of the equation $z^4 + z^3 + (-36 + 15i)z^2 + mz = 0$ are the vertices of a square then $(\lambda + m)$ can be equal to
Step-by-Step Solution
Key Concept: Subtract cases with common vertices or sides from total pairs to find disjoint selections.
In an $8 \times 7$ grid of $2 \times 2$ squares, there are $7 \times 7 = 49$ such squares. Two squares share a common vertex in $7 \times 7 \times 2 = 98$ ways. Two squares sharing a common side occurs in $7 \times 8 \times 2 = 112$ ways. Thus, the number of ways to select two squares sharing neither vertex nor side is $\binom{49}{2} - 98 - 112 = 1176 - 210 = 1806$.
Correct Answer: 1,2