Discussion Forum

 If  $|z| \geq 3,$ then the least value of  $|z+\frac{1}{4}|$  is 

Answer:

Explanation:

$|z+\frac{1}{4}|$

= $|z-\left(\frac{-1}{4}\right)| \geq|z|-|\frac{-1}{4}|$

=  $|(-z)-\left(\frac{1}{4}\right)| \geq|3-\frac{1}{4}|=\frac{11}{4}$

$\therefore$      $|z+\frac{1}{4}| \geq\frac{11}{4}$