Question

If arg $z=\frac{\pi }{2}$, then $z$ is

• A. Purely real
• B. Purely imaginary
• C. A complex number
• D. Equal to $-i$

Answer 1

Answer: (B), (C)

Purely imaginary
A complex number

let $z=x+iy$
$\therefore arg\left(z\right)=ta{n}^{-1}\left(y/x\right)=\pi /2$
i.e. $x=0$
hence $z$ lies on imaginary axis

Hence, $z$ is purely imaginary. It is also a complex number.
Hence, options B and C are correct.