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Q)

Express the given complex number in the form $\;a+ib :\;[( \normalsize \large\frac{1}{3} +\normalsize i \normalsize \large\frac{7}{3}) + (\normalsize 4 + \normalsize i \normalsize \large\frac{1}{3})-( \normalsize -\large\frac{4}{3}+ \normalsize i)]$

$(a)\;\large\frac{19}{3} +i \large\frac{17}{3}\qquad(b)\;\large\frac{19}{3} +i \large\frac{5}{3}\qquad(c)\;\large\frac{16}{3} +i \large\frac{10}{3}\qquad(d)\;\large\frac{17}{3} +i \large\frac{5}{3}$

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A)
Answer : $\;\large\frac{17}{3} +i \large\frac{5}{3}$
Explanation :
$[(\large\frac{1}{3}+i\large\frac{7}{3}) + (4 +i\large\frac{1}{3})-(-\large\frac{4}{3}+i)]=\large\frac{1}{3}+\large\frac{7}{3}i +4 +\large\frac{1}{3}i +\large\frac{4}{3}i -i$
$ = (\large\frac{1}{3} +4+ \large\frac{4}{3} ) +i( \large\frac{7}{3} + \large\frac{1}{3} -1 ) $
$=\large\frac{17}{3} +i \large\frac{5}{3}\;.$
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