Question

Simplify: (3 + 4i) + (2 - 3i) - (5 - 6i)

Answer 1

The answer is:  " 7 i " .
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Explanation:
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(3 + 4i) + (2 - 3i) - (5 - 6i) =

(3 + 4i) + 1(2 - 3i) - 1(5 - 6i) ;   ←  Note that the coefficient, "1" is implied; 
                    since any value, multiplied by "1" , results in that same value.
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Note the "distributive property" of multiplication:
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a(b + c) = ab + ac ;

a(b – c) = ab – ac .
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We have:

(3 + 4i) + 1(2 - 3i) - 1(5 - 6i) ;

Start with:

 " + 1(2 - 3i) "  =  (1*2) - (1*3i)  = 2 - 3i ; 

Then, we examine:

 " - 1(5 - 6i) "  =  (-1*5) + (-1 * -6i) = -5 + (+6i) =  -5 + 6i ; 
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And we rewrite the entire expression:
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   3 + 4i + 2 - 3i - 5 + 6i  ; 

Combine the "like terms" ; as follows:

   3 + 2 - 5 = 5  - 5 = 0 ; 

   4i - 3i + 6i = 1 i  + 6i = 7 i ; 

     0 + 7i = 7i .
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The answer is:  " 7 i " .
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Answer 2

(3 + 2 - 5) and (4i - 3i + 6i)
= 0 + 7i