$\frac{1}{0.5 + i} + \frac{2}{3 + 2 i} = \frac{6 - 17 i}{13}$

Explanation

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$\frac{1}{0.5 + i} + \frac{2}{3 + 2 i} \overset{◯}{1} \frac{4 i + 3}{2 i ^{2} + 3 i} \overset{◯}{2} \frac{4 i + 3}{- 2 + 3 i} \overset{◯}{3} \frac{6 - 17 i}{13}$
①	Add $\frac{1}{0 + i}$ and $\frac{2}{3 + 2 i}$ to get $\frac{4 i + 3}{2 i ^{2} + 3 i}$ . To add raitonal expressions, both fractions must have the same denominator. We can create a common denominator by multiplying the first fraction by $2 i + 3$ and the second by $i$ . $\frac{1}{0 + i} + \frac{2}{3 + 2 i} = \frac{1 \cdot ( 2 i + 3 )}{( 0 + i ) \cdot ( 2 i + 3 )} + \frac{2 \cdot i}{( 3 + 2 i ) \cdot i} = = \frac{2 i + 3}{0 i 0 + 2 i ^{2} + 3 i} + \frac{2 i}{0 i 0 + 2 i ^{2} + 3 i} = \frac{4 i + 3}{2 i ^{2} + 3 i}$
②	$2 i^{2} = 2 \cdot (- 1) = - 2$
③	Divide $3 + 4 i$ by $- 2 + 3 i$ to get $\frac{6 - 17 i}{13}$ . ( view steps )

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0.5+i1​+3+2i2​=136−17i​

$\frac{1}{0.5 + i} + \frac{2}{3 + 2 i} = \frac{6 - 17 i}{13}$