Question

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

Answer 1

`(17/3)+i(5/3)`

Explanation:

Adding the real parts

`1/3+4+4/3=17/3`

Adding the imaginary parts

`7/3+1/3-1=5/3`

Hence, the sum is

`Re (z)+Im (z)`

where `z` is a complex number.

Answer 2

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: `[(1/3+i7/3)+(4+i1/3)]-(-4/3+i)`

Distribute the implied -1:

`[(1/3+i7/3)+(4+i1/3)]+(4/3-i)`

Remove the braces and parenthesis:

`1/3+i7/3+4+i1/3+4/3-i`

Combine like terms:

`1/3+4+4/3+i(7/3+1/3-1)`

`17/3+i5/3`