(d)$\left( {\frac{1}{{1 – 2i}} + \frac{3}{{1 + i}}} \right)\,\,\left( {\frac{{3 + 4i}}{{2 – 4i}}} \right)$
$ = \left[ {\frac{{1 + 2i}}{{{1^2} + {2^2}}} + \frac{{3 – 3i}}{{{1^2} + {1^2}}}} \right]\,\left[ {\frac{{6 – 16 + 12i + 8i}}{{{2^2} + {4^2}}}} \right]$
$ = \left( {\frac{{2 + 4i + 15 – 15i}}{{10}}} \right)\,\,\left( {\frac{{ – 1 + 2i}}{2}} \right)$
$ = \frac{{(17 – 11i)( – 1 + 2i)}}{{20}} = \frac{{5 + 45i}}{{20}} = \frac{1}{4} + \frac{9}{4}i$.