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If z be a complex number satisfying | z – 4 + 8 i | = 4 , then the least and the greatest value of | z + 2 | are respectively (where i = - 1 )

Options

  1. A7 and 16
  2. B8 and 17
  3. C6 and 14
  4. D5 and 13

Correct answer

C. 6 and 14

Step-by-step solution

| z + 2 | = | z + 2 – 4 + 8 i + 4 – 8 i | | z + 2 | = | z – 4 + 8 i + 6 – 8 i | z + 2 ≤ | z - 4 + 8 i | + | 6 - 8 i | ≤ 4 + 10 = 14 | z + 2 | = | z + 2 – 4 + 8 i + 4 – 8 i | ≥ | z - 4 + 8 i | - | 6 - 8 i | ≥ 4 - 10 = 6

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