argleft( frac{3 + i}{2 - i} + frac{3 - i}{2 + | vedclass

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Question

(C) Let $z = \frac{3 + i}{2 - i} + \frac{3 - i}{2 + i}$.First,simplify the expression by finding a common denominator:$z = \frac{(3 + i)(2 + i) + (3 -

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$0$

Vedclass · Answer

(C) Let $z = \frac{3 + i}{2 - i} + \frac{3 - i}{2 + i}$.First,simplify the expression by finding a common denominator:$z = \frac{(3 + i)(2 + i) + (3 - i)(2 - i)}{(2 - i)(2 + i)}$$z = \frac{(6 + 3i + 2i + i^2) + (6 - 3i - 2i + i^2)}{4 - i^2}$Since $i^2 = -1$,we have:$z = \frac{(6 + 5i - 1) + (6 - 5i - 1)}{4 - (-1)}$$z = \frac{5 + 5i + 5 - 5i}{5} = \frac{10}{5} = 2$.Now,find the argument of $z = 2$:$arg(2) = 0$ (since $2$ is a positive real number).Therefore,the correct option is $C$.

$arg\left( \frac{3 + i}{2 - i} + \frac{3 - i}{2 + i} \right)$ is equal to

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