Express the given complex number in the form a + ib:

Question:

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

Solution:

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

$=\frac{1}{3}+\frac{7}{3} i+4+\frac{1}{3} i+\frac{4}{3}-i$

$=\left(\frac{1}{3}+4+\frac{4}{3}\right)+i\left(\frac{7}{3}+\frac{1}{3}-1\right)$

$=\frac{17}{3}+i \frac{5}{3}$

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