$(1 + i) (2 + a i) + (2 + 3 i) (3 + i) = x + i y, x, y b e l o n g s t o R a n d x e q u a l y, t h e n a e q u a l$

$5$

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$- 4$

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$- 5$

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$4$

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Solution

The correct option is B
$- 4$

Explanation for the correct option:
Step 1. Write the given expression:
$(1 + i) (2 + a i) + (2 + 3 i) (3 + i) = x + i y$
$\Rightarrow 2 + 2 i + a i - a + 6 + 9 i + 2 i - 3 = x + i y$
$\Rightarrow$ $5 - a + (13 + a) i = x + i y$
Step 2. Equate real and imaginary parts:
$\Rightarrow 5 - a = x, 13 + a = y$
According to the question $x = y$
Therefore, $5 - a = 13 + a$
$\Rightarrow$ $2 a = - 8$
$\Rightarrow$ $a = - 4$
Hence, Option ‘B’ is Correct.

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