If $z$ is a complex number satisfying $z - 12 = i (9 - 2 ¯ ¯ ¯ z),$ then the value of $z + ¯ ¯ ¯ z$ is

10

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4

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6

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8

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Solution

The correct option is B $4$
Given equation is $z - 12 = i (9 - 2 ¯ ¯ ¯ z)$
Let $z = a + i b$
Now,
$z - 12 = i (9 - 2 ¯ ¯ ¯ z) \Rightarrow z + 2 i ¯ ¯ ¯ z = 12 + 9 i \Rightarrow (a + i b) + 2 i (a - i b) = 12 + 9 i \Rightarrow (a + 2 b) + i (b + 2 a) = 12 + 9 i \Rightarrow a + 2 b = 12, b + 2 a = 9 \Rightarrow a = 2, b = 5 \Rightarrow z = 2 + 5 i ∴ z + ¯ ¯ ¯ z = 2 R e (z) = 4$

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