Express the complex number [ ( 1 3 + 7 3 i ) + ( 4 + 1 3 i ) ] - … - Vidyadip

Question

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

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Answer

$\left[ {\left( {\frac{1}{3} + \frac{7}{3}i} \right) + \left( {4 + \frac{1}{3}i} \right)} \right] - \left[ {\frac{{ - 4}}{3} + i} \right]$
$ =\left(\frac13+4+\frac43\right)+\left(\frac73i+\frac13i\;-i\right)$
$\;=\left(\frac13+\frac{4\times3}3+\frac43\right)+\left(\frac73i\;+\frac i3-\frac{3i}3\right)$
$=\left(\frac{1+12+4}3\right)+\left(\frac{7i+i\;-3i}3\right)$
$ = \frac{{17}}{3} + \frac{5}{3}i$

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