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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