Question

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

Answer 1

$[(\frac{1}{3}+i\frac{7}{3})+(4+i\frac{1}{3})]-(\frac{-4}{3}+i)$
$=\frac{1}{3}+\frac{7}{3}i+4+\frac{1}{3}i+\frac{4}{3}-i$
$=(\frac{1}{3}+4+\frac{4}{3})+i(\frac{7}{3}+\frac{1}{3}-1)$
$=\frac{17}{3}+i\frac{5}{3}=a+ib$
where, $a=\frac{17}{3}$ and $b=\frac{5}{3}$