How do you evaluate [ (\frac { 1} { 3} + i \frac { 7} { 3} ) + ( 4+ i \frac { 1} { 3} ) ] - ( - \frac { 4} { 3} + i )?

Jan 30, 2018

$\left(\frac{17}{3}\right) + i \left(\frac{5}{3}\right)$

Explanation:

$\frac{1}{3} + 4 + \frac{4}{3} = \frac{17}{3}$

$\frac{7}{3} + \frac{1}{3} - 1 = \frac{5}{3}$

Hence, the sum is

$R e \left(z\right) + I m \left(z\right)$

where $z$ is a complex number.

Jan 30, 2018

Use the distributive property to distribute the implied -1 through the parenthesis of the last term, then remove the braces and parenthesis and combine like terms.

Explanation:

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

Distribute the implied -1:

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

Remove the braces and parenthesis:

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

Combine like terms:

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

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