$$\frac{2+3i}{4-i}$$
$\frac{5}{17}+\frac{14}{17}i\approx 0.294117647+0.823529412i$
$$\frac{\left(2+3i\right)\left(4+i\right)}{\left(4-i\right)\left(4+i\right)}$$
$$\frac{\left(2+3i\right)\left(4+i\right)}{4^{2}-i^{2}}$$
$$\frac{\left(2+3i\right)\left(4+i\right)}{17}$$
$$\frac{2\times 4+2i+3i\times 4+3i^{2}}{17}$$
$$\frac{2\times 4+2i+3i\times 4+3\left(-1\right)}{17}$$
$$\frac{8+2i+12i-3}{17}$$
$$\frac{8-3+\left(2+12\right)i}{17}$$
$$\frac{5+14i}{17}$$
$$\frac{5}{17}+\frac{14}{17}i$$
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$\frac{5}{17} = 0.29411764705882354$
$$Re(\frac{\left(2+3i\right)\left(4+i\right)}{\left(4-i\right)\left(4+i\right)})$$
$$Re(\frac{\left(2+3i\right)\left(4+i\right)}{4^{2}-i^{2}})$$
$$Re(\frac{\left(2+3i\right)\left(4+i\right)}{17})$$
$$Re(\frac{2\times 4+2i+3i\times 4+3i^{2}}{17})$$
$$Re(\frac{2\times 4+2i+3i\times 4+3\left(-1\right)}{17})$$
$$Re(\frac{8+2i+12i-3}{17})$$
$$Re(\frac{8-3+\left(2+12\right)i}{17})$$
$$Re(\frac{5+14i}{17})$$
$$Re(\frac{5}{17}+\frac{14}{17}i)$$
$$\frac{5}{17}$$
