- Home
- Standard 11
- Mathematics
4-1.Complex numbers
easy
${\mathop{\rm Re}\nolimits} \frac{{{{(1 + i)}^2}}}{{3 - i}}$ =
A
$- 1/5$
B
$1/5$
C
$1/10$
D
$-1/10$
Solution
(a) ${\mathop{\rm Re}\nolimits} \left[ {\frac{{{{(1 + i)}^2}}}{{3 – i}}} \right] = {\mathop{\rm Re}\nolimits} \left[ {\left( {\frac{{2i}}{{3 – i}}} \right)\,\,\left( {\frac{{3 + i}}{{3 + i}}} \right)} \right]$
${\mathop{\rm Re}\nolimits} \left[ {\frac{{{{(1 + i)}^2}}}{{3 – i}}} \right] = {\mathop{\rm Re}\nolimits} \left[ {\left( {\frac{{2i}}{{3 – i}}} \right)\left( {\frac{{3 + i}}{{3 + i}}} \right)} \right]$
$ = {\mathop{\rm Re}\nolimits} \left[ {\frac{{6i – 2}}{{9 + 1}}} \right] = {\mathop{\rm Re}\nolimits} \left[ { – \frac{2}{{10}} + \frac{6}{{10}}i} \right] = – \frac{1}{5}$.
Standard 11
Mathematics
