$$\frac{2+i}{3+2i}$$
$\frac{8}{13}-\frac{1}{13}i\approx 0.615384615-0.076923077i$
$$\frac{\left(2+i\right)\left(3-2i\right)}{\left(3+2i\right)\left(3-2i\right)}$$
$$\frac{\left(2+i\right)\left(3-2i\right)}{3^{2}-2^{2}i^{2}}$$
$$\frac{\left(2+i\right)\left(3-2i\right)}{13}$$
$$\frac{2\times 3+2\times \left(-2i\right)+3i-2i^{2}}{13}$$
$$\frac{2\times 3+2\times \left(-2i\right)+3i-2\left(-1\right)}{13}$$
$$\frac{6-4i+3i+2}{13}$$
$$\frac{6+2+\left(-4+3\right)i}{13}$$
$$\frac{8-i}{13}$$
$$\frac{8}{13}-\frac{1}{13}i$$
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$\frac{8}{13} = 0.6153846153846154$
$$Re(\frac{\left(2+i\right)\left(3-2i\right)}{\left(3+2i\right)\left(3-2i\right)})$$
$$Re(\frac{\left(2+i\right)\left(3-2i\right)}{3^{2}-2^{2}i^{2}})$$
$$Re(\frac{\left(2+i\right)\left(3-2i\right)}{13})$$
$$Re(\frac{2\times 3+2\times \left(-2i\right)+3i-2i^{2}}{13})$$
$$Re(\frac{2\times 3+2\times \left(-2i\right)+3i-2\left(-1\right)}{13})$$
$$Re(\frac{6-4i+3i+2}{13})$$
$$Re(\frac{6+2+\left(-4+3\right)i}{13})$$
$$Re(\frac{8-i}{13})$$
$$Re(\frac{8}{13}-\frac{1}{13}i)$$
$$\frac{8}{13}$$
