$$(\frac{1}{2}+\frac{3}{2}i)+(\frac{-3}{4}+\frac{1}{4}i)$$
$-\frac{1}{4}+\frac{7}{4}i=-0.25+1.75i$
$$\frac{-3}{4}+\frac{1}{2}+\left(\frac{3}{2}+\frac{1}{4}\right)i$$
$$\frac{-3}{4}+\frac{1}{2}+\frac{7}{4}i$$
$$-\frac{3}{4}+\frac{1}{2}+\frac{7}{4}i$$
$$-\frac{1}{4}+\frac{7}{4}i$$
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$-\frac{1}{4} = -0.25$
$$Re(\frac{-3}{4}+\frac{1}{2}+\left(\frac{3}{2}+\frac{1}{4}\right)i)$$
$$Re(\frac{-3}{4}+\frac{1}{2}+\frac{7}{4}i)$$
$$Re(-\frac{3}{4}+\frac{1}{2}+\frac{7}{4}i)$$
$$Re(-\frac{1}{4}+\frac{7}{4}i)$$
$$-\frac{1}{4}$$
