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 )

Question

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 ), 7 and 16, 8 and 17, 6 and 14, 5 and 13

MARKS App · Accepted Answer

| 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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