Math, asked by cashew74, 10 months ago

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

Answers

Answered by Divyansh50800850
2

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Attachments:
Answered by ItsTogepi
3

\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}

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