Question

If $|\pi -\text{arg}z|<\frac{\pi }{4},$ then, find the range of values of arg$\left(z\right)$.

• A. $-\frac{5\pi }{4}>\text{arg}z>-\frac{3\pi }{4}$
• B. $\frac{\pi }{4}>\text{arg}z>\frac{3\pi }{4}$
• C. $\frac{3\pi }{4}<\text{arg}z<\frac{5\pi }{4}$
• D. $-\frac{3\pi }{4}>\text{arg}z>-\frac{\pi }{4}$

Answer 1

The correct option is C $\frac{3\pi }{4}<\text{arg}z<\frac{5\pi }{4}$

$|\pi -argz|<\pi /4.$
$\Rightarrow -\pi /4<\pi -argz<\pi /4$
$\Rightarrow -5\pi /4<-argz<-3\pi /4$
$\Rightarrow 5\pi /4>argz>3\pi /4$
$\Rightarrow 3\pi /4<argz<5\pi /4$
Ans: c