Question

If the argument of a complex number is $\frac{\pi }{2}$, then the number is:

• A. Purely imaginary
• B. Purely real
• C. $0$
• D. Neither real nor imaginary

Answer 1

Answer: (A)

Purely imaginary

Let the complex number be $z$.
Hence
$z=|z|e^{i\arg \left(z\right)}$
$=|z|e^{i\frac{\pi }{2}}$
$=|z|(\cos \frac{\pi }{2}+i\sin \frac{\pi }{2})$
$=i|z|$
Hence the complex number is purely imaginary.