Question

Statement-1 : Roots of the equation $(1+z)^6+z^6=0$ are collinear.
Statement-2 : If $z_1, z_2, z_3$ are in A.P. then points represented by $z_1, z_2, z_3$ are collinear

• A. Both the statements are true.
• B. Statement-I is true, but Statement-II is false.
• C. Statement-I is false, but Statement-II is true.
• D. Both the statements are false.

Answer 1

Answer: (A)

Statement -1 $(1+z)^6=-z^6$
take modulus
$|1+z|^6=|z|^6$
$\left|\frac{1+z}{z}\right|=1 $ which is straight line
Statement $-2 z_2=\frac{z_1+z_3}{2}$
$\therefore z_2$ is mid point of line joining $z_1 \& z_3$.
Hence $z_1, z_2, z_3$ are collinear