Question 274544
you simplify and combine like terms.


(-6 + 2i) + (-4 - 4i) becomes:


-6 + 2i -4 - 4i after you remove the parentheses (be careful of the signs).


combine like terms and you get -10 - 2i.


(9 + 6i) - (5 + i) becomes:


9 + 6i - 5 - i after you remove the parentheses (be careful of the signs).


combine like terms and you get 4 + 5i.


you treat the i the same way you would treat another variable.


The only difference is that at the end you can translate the i to whatever value it is based on the fact that:


{{{i = sqrt(-1) = i}}}


{{{i^2 = sqrt(-1)^2 = -1}}}


{{{i^3 = sqrt(-1)^3 = sqrt(-1)^2 * sqrt(-1) = -1 * sqrt(-1) = -1*i = -i}}}


{{{i^4 = sqrt(-1)^4 = sqrt(-1)^2 * sqrt(-1)^2 = -1 * -1 = 1}}}


example:


add i^3 + i^2 + i + 3i^3 + 3i^2 + 3i


you combine like terms to get:


4i^3 + 4i^2 + 4i


the i was treated just like another variable.


at the end, however, you can translate the i to it's simplest terms


since i^3 = -i and i^2 = -1, then:


4i^3 + 4i^2 + 4i becomes:


-4i -4 + 4i in its simplest terms.


when you combine like terms again (after simplification), then it becomes:


-4


Here's a reference for you.


<a href = "http://www.purplemath.com/modules/complex.htm" target = "_blank">http://www.purplemath.com/modules/complex.htm</a>