Express the following in the form of $a + b i$ and the value of $a$ and $b$ : $\frac{2 + i}{(3 - i) (1 + 2 i)}$

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Solution

$\frac{2 + i}{(3 + 6 i) (1 + 2 i)} = \frac{2 + i}{5 + 5 i} (i^{2} = - 1) = \frac{2 + i}{5 + 5 i} \times \frac{5 - 5 i}{5 - 5 i} = \frac{15 - 5 i}{50} = \frac{3}{10} - \frac{1}{10} i$

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