$$\frac { 2 - 7 i } { 4 + 5 i }$$
$-\frac{27}{41}-\frac{38}{41}i\approx -0.658536585-0.926829268i$
$$\frac{\left(2-7i\right)\left(4-5i\right)}{\left(4+5i\right)\left(4-5i\right)}$$
$$\frac{\left(2-7i\right)\left(4-5i\right)}{4^{2}-5^{2}i^{2}}$$
$$\frac{\left(2-7i\right)\left(4-5i\right)}{41}$$
$$\frac{2\times 4+2\times \left(-5i\right)-7i\times 4-7\left(-5\right)i^{2}}{41}$$
$$\frac{2\times 4+2\times \left(-5i\right)-7i\times 4-7\left(-5\right)\left(-1\right)}{41}$$
$$\frac{8-10i-28i-35}{41}$$
$$\frac{8-35+\left(-10-28\right)i}{41}$$
$$\frac{-27-38i}{41}$$
$$-\frac{27}{41}-\frac{38}{41}i$$
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$-\frac{27}{41} = -0.6585365853658537$
$$Re(\frac{\left(2-7i\right)\left(4-5i\right)}{\left(4+5i\right)\left(4-5i\right)})$$
$$Re(\frac{\left(2-7i\right)\left(4-5i\right)}{4^{2}-5^{2}i^{2}})$$
$$Re(\frac{\left(2-7i\right)\left(4-5i\right)}{41})$$
$$Re(\frac{2\times 4+2\times \left(-5i\right)-7i\times 4-7\left(-5\right)i^{2}}{41})$$
$$Re(\frac{2\times 4+2\times \left(-5i\right)-7i\times 4-7\left(-5\right)\left(-1\right)}{41})$$
$$Re(\frac{8-10i-28i-35}{41})$$
$$Re(\frac{8-35+\left(-10-28\right)i}{41})$$
$$Re(\frac{-27-38i}{41})$$
$$Re(-\frac{27}{41}-\frac{38}{41}i)$$
$$-\frac{27}{41}$$
