Question

The greatest and the least value of $|z_1+z_2|$ if $z_1=24+7i$ and $|z_2|=6$ are respectively

• A. $31,19$
• B. $25,19$
• C. $31,25$
• D. $31$, $-$$19$

Answer 1

The correct option is A $31,19$

We know that

$|z_1+z_2|⩽|z_1|+|z_2|$

$⩽|\sqrt{{24}^2+7^2}+6|$

$⩽|25+6|$

$⩽31$

also $|z_1+z_2|⩾||z_1|-|z_1||$

$⩾|25-6|$

$⩾19$

Thus $19⩽|z_1+z_2|⩽31$