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Express each of the complex number in the form a+ib. (7) [(1/3+i7/3)+(4+i1/3)]-(-4/3+i)

Express each of the complex number in the form  a+ib.

Q : 7    \left [ \left ( \frac{1}{3}+i\frac{7}{3} \right )+\left ( 4+i\frac{1}{3} \right ) \right ]-\left ( -\frac{4}{3}+i \right )

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Given problem is 
\left [ \left ( \frac{1}{3}+i\frac{7}{3} \right )+\left ( 4+i\frac{1}{3} \right ) \right ]-\left ( -\frac{4}{3}+i \right )
Now, we will reduce it into

\left [ \left ( \frac{1}{3}+i\frac{7}{3} \right )+\left ( 4+i\frac{1}{3} \right ) \right ]-\left ( -\frac{4}{3}+i \right ) = \frac{1}{3}+i\frac{7}{3} + 4+i\frac{1}{3} + \frac{4}{3}-i  
                                                                                    =\frac{1+4+12}{3}+i\frac{(7+1-3)}{3}
                                                                                    =\frac{17}{3}+i\frac{5}{3}                           

Therefore, the answer is  \frac{17}{3}+i\frac{5}{3}

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