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Question:

If z is a complex number such that |z| ≥ 2, then the minimum value of |z + 12| is equal to 52, lies in the interval (1, 2), is strictly greater than 52, is strictly greater than 32 but less than 52

is equal to 52

is strictly greater than 52

is strictly greater than 32 but less than 52

lies in the interval (1, 2)

Solution:

Given |z| ≥ 2 ∴ |z + 12| ≥ ||z| - |12|| [∵ |z₁ + z₂| ≥ |z₁| - |z₂|] ∴ |z + 12| ≥ |2 - 12| ≥ 10 Hence, minimum value of |z + 12| is 10 which indicates that it lies in the interval (1, 2)