Question

The volve
of 1 +i /(3+4i) is​

Answer 1

$\huge{\green{\boxed{\mathcal{\red{ANSWER :-}}}}}$

$\frac{1 + i}{3 + 4i} = \frac{1 + i}{3 + 4i} \times \frac{3 - 4i}{3 - 4i} \\ = \frac{3 + 3i - 4i - 4 {i}^{2} }{ {3}^{2} - {(4i)}^{2} } \\ = \frac{3 - i - 4 {i}^{2} }{9 - 16 {i}^{2} } \\ as \: we \: know \: the \: value \: of \: {i}^{2} = - 1 \\ = \frac{3 - i + 4}{9 + 16} \\ = \frac{7 - i}{25}$

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