$$\frac{-3+4i}{5-4i}$$
$-\frac{31}{41}+\frac{8}{41}i\approx -0.756097561+0.195121951i$
$$\frac{\left(-3+4i\right)\left(5+4i\right)}{\left(5-4i\right)\left(5+4i\right)}$$
$$\frac{\left(-3+4i\right)\left(5+4i\right)}{5^{2}-4^{2}i^{2}}$$
$$\frac{\left(-3+4i\right)\left(5+4i\right)}{41}$$
$$\frac{-3\times 5-3\times \left(4i\right)+4i\times 5+4\times 4i^{2}}{41}$$
$$\frac{-3\times 5-3\times \left(4i\right)+4i\times 5+4\times 4\left(-1\right)}{41}$$
$$\frac{-15-12i+20i-16}{41}$$
$$\frac{-15-16+\left(-12+20\right)i}{41}$$
$$\frac{-31+8i}{41}$$
$$-\frac{31}{41}+\frac{8}{41}i$$
Show Solution
Hide Solution
$-\frac{31}{41} = -0.7560975609756098$
$$Re(\frac{\left(-3+4i\right)\left(5+4i\right)}{\left(5-4i\right)\left(5+4i\right)})$$
$$Re(\frac{\left(-3+4i\right)\left(5+4i\right)}{5^{2}-4^{2}i^{2}})$$
$$Re(\frac{\left(-3+4i\right)\left(5+4i\right)}{41})$$
$$Re(\frac{-3\times 5-3\times \left(4i\right)+4i\times 5+4\times 4i^{2}}{41})$$
$$Re(\frac{-3\times 5-3\times \left(4i\right)+4i\times 5+4\times 4\left(-1\right)}{41})$$
$$Re(\frac{-15-12i+20i-16}{41})$$
$$Re(\frac{-15-16+\left(-12+20\right)i}{41})$$
$$Re(\frac{-31+8i}{41})$$
$$Re(-\frac{31}{41}+\frac{8}{41}i)$$
$$-\frac{31}{41}$$
