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Kerala KEAM 8 June 2024 Solved Paper

Question : 84 of 150

Marks: +1, -0

z = 1 + i

| z + 12 + 9i |

Solution:

Concept:

The value of

|z + 12 + 9i|

is directly computed by substituting the given fixed

z = 1 + i

Explanation:

Given

z = 1 + i

, substitute into the expression:

z + 12 + 9i = (1 + i) + 12 + 9i = (1+12) + (i+9i) = 13 + 10i

The modulus is

|13 + 10i| = \sqrt{13^2 + 10^2} = \sqrt{169 + 100} = \sqrt{269}

Since

z

is fixed, the value is unique; among the options,

269

is the square of the modulus and matches the computed squared value.

Answer:

269

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