1) If $|z| \geq 3,$ then the least value of $|z+\frac{1}{4}| $ is A) $\frac{11}{2} $ B) $\frac{11}{4} $ C) 3 D) $\frac{1}{4} $ Answer: Option BExplanation:$|z+\frac{1}{4}| $ = $|z-\left(\frac{-1}{4}\right)| \geq|z|-|\frac{-1}{4}|$ = $|(-z)-\left(\frac{1}{4}\right)| \geq|3-\frac{1}{4}|=\frac{11}{4}$ $\therefore$ $|z+\frac{1}{4}| \geq\frac{11}{4}$
