Question

If $|z-4+3i|\underset{–}{<}2,$ then the least and the greatest values of |z| are

• A. $3,7$
• B. $4,7$
• C. $3,9$
• D. $4,5$

Answer 1

The correct option is A $3,7$

we have,

$|z-a+ib|\le c$

max value of $z=c+\sqrt{a^2+b^2}$

min value of $z=c-\sqrt{a^2+b^2}$

Given,

$|z-4+3i|\le 2$

max value of $|z|=|2+\sqrt{4^2+3^2}|=7$

min value of $|z|=|2-\sqrt{4^2+3^2}|=3$