document.write( "Question 686199: (-3-8i)+(-5-7i) \n" ); document.write( "

Algebra.Com's Answer #424978 by RedemptiveMath(80) $\"\"$ $\"About$

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The form of this expression can be written in the form (a+bi)+(c+di) concerning the addition of complex quantities. This simplifies to (a+c)+(b+d)i. Being mindful of signs in this expression, we solve by simply combining like terms:\r
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\n" ); document.write( "\n" ); document.write( "(-3-8i)+(-5-7i) =
\n" ); document.write( "[-3+(-5)] + [-8i+(-7i)] =
\n" ); document.write( "(-3-5) + (-8-7)i =
\n" ); document.write( "-8 + (-15)i =
\n" ); document.write( "-8 - 15i or -1(8+15i).\r
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\n" ); document.write( "\n" ); document.write( "A way you can think of adding or subtracting complex numbers is imagining the imaginary to be like a variable \"x\" in normal algebraic computation. If you had an expression (-3-8x) and an expression (-5-7x), you would combine them in addition by adding the constants, (-3) and (-5), together and the coefficients, (-8) for the first x and (-7) for the second x, together. Thus, you would receive (-8-15x) or -1(8+15x) as simplified answers. It would be dependent on your teacher whether or not you factor out the -1 in the latter, but both would serve as equivalent expressions. It may be unconventional to write a complex quantity with a factored -1. This would also be dependent on your teacher and course. \r
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\n" ); document.write( "\n" ); document.write( "You MUST be careful if you choose to think of these complex expressions in this way. This method does not give an excuse for calling the imaginary simply a variable by comparison of outputs. A variable can stand for anything in a context, but imaginaries stand for (sqrt)(-1). That's why in multiplication and division you must be mindful of squares, cubes, and so forth of i. \n" ); document.write( "

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