Let $z$ be a non-zero complex number such that $\frac { z } { 1 + z }$ is purely imaginary. Then (a) $z$ is neither real nor purely imaginary (b) $z$ is real (c) $z$ is purely imaginary (d) none of the above.
(a) Check (b) and (c) are false, and then that (a) is true.
Let $z$ be a non-zero complex number such that $\frac { z } { 1 + z }$ is purely imaginary. Then\\
(a) $z$ is neither real nor purely imaginary\\
(b) $z$ is real\\
(c) $z$ is purely imaginary\\
(d) none of the above.