Question

Z is a complex number and if
$|z + 5| \leqslant 6$
then determine the greatest and smallest value of
$|z + 2|$
​

Answer 1

your answer is in the attachment photo

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Answer 2

$\huge\underline\mathfrak\color{lavender}Given:$

• Z is a complex number.
• $\sf{ |z + 5| \leqslant 6}$

$\huge\underline\mathfrak\color{pink}To \: Find:$

• The greatest and smallest value of $\sf{ |z + 2| }$

$\huge\underline\mathfrak\color{plum}Solution:$

$\sf\color{green}{Z \: is \: a \: complex \: number.}$

$\sf{ |z| \geqslant 0}$

$\sf\green{And}$

$\sf{ |z + 2| \geqslant 0}$

$\sf\green{Now, \: by \: equalling \: real \: and \: unreal \: numbers, }$

$\sf\green{ we \: get,}$

$\sf{ |z + 2| = |(z + 5) - 3| } \leqslant |z + 5| + ( - 3)$

$\sf{\implies |z + 2| \leqslant 6 + 3}$

$\sf{\implies |z + 2| \leqslant 9}$

$\sf{ |z + 2| = 9}$

$\sf\green{Therefore,}$

$\sf{0 \leqslant |z + 2| \leqslant 9}$

$\sf{ |z + 2| = 0}$

$\sf\color{lawngreen}{Hence \: the \: greatest \: value \: of \: |z + 2| = 9} \\ \sf\color{lawngreen}{and \: the \: smallest \: value \: |z + 2| = 0 }$

$\huge\underline\mathfrak\pink{Thank \: uhh}$