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If | Z + 4 | ≤ 3 , Then Find the Greatest and Least Values of | Z + 1 | .

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प्रश्न

If \[\left| z + 4 \right| \leq 3\], then find the greatest and least values of \[\left| z + 1 \right|\].

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उत्तर

\[\left| z + 1 \right| = \left| z + 4 - 3 \right|\]

\[ \leq \left| z + 4 \right| + \left| - 3 \right|\]

\[ \leq 3 + 3\]

\[ = 6\]

\[\text { Also }, \]

\[\left| z + 1 \right| \geq 0\]

\[\text { Thus }, 0 \leq \left| z + 1 \right| \leq 6 .\]

Hence, the greatest and least values of 

\[\left| z + 1 \right|\] is 6 and 0.
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अध्याय 13: Complex Numbers - Exercise 13.5 [पृष्ठ ६३]

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आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 13 Complex Numbers
Exercise 13.5 | Q 18 | पृष्ठ ६३

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