$$\frac{ 1 }{ 4+7i }$$
$\frac{4}{65}-\frac{7}{65}i\approx 0.061538462-0.107692308i$
$$\frac{1\left(4-7i\right)}{\left(4+7i\right)\left(4-7i\right)}$$
$$\frac{1\left(4-7i\right)}{4^{2}-7^{2}i^{2}}$$
$$\frac{1\left(4-7i\right)}{65}$$
$$\frac{4-7i}{65}$$
$$\frac{4}{65}-\frac{7}{65}i$$
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$\frac{4}{65} = 0.06153846153846154$
$$Re(\frac{1\left(4-7i\right)}{\left(4+7i\right)\left(4-7i\right)})$$
$$Re(\frac{1\left(4-7i\right)}{4^{2}-7^{2}i^{2}})$$
$$Re(\frac{1\left(4-7i\right)}{65})$$
$$Re(\frac{4-7i}{65})$$
$$Re(\frac{4}{65}-\frac{7}{65}i)$$
$$\frac{4}{65}$$
