Question

The set of points in $C$ satisfying the inequality $|arg\left(z\right)-\pi /2|<\pi /2$ is given by

• A. $\{z:Re(z)>0\}$
• B. $\{z:In(z)<0\}$
• C. $\{z:Im(z)>0\}$
• D. $\{z:Re(z)=Im(z\left)\right\}$

Answer 1

Answer: (C)

$\{z:Im(z)>0\}$

$C:|arg\left(z\right)-\frac{\pi }{2}|<\frac{\pi }{2}$

$|arg\left(z\right)-\frac{\pi }{2}|<\frac{\pi }{2}$

$\left|arg\left(z\right)\right|>\frac{\pi }{4}$

$\Rightarrow \{z:Im\left(z\right)>0\}$

Hence, the answer is $\{z:Im\left(z\right)>0\}.$