Question 686199: (-3-8i)+(-5-7i)
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! 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:
(-3-8i)+(-5-7i) =
[-3+(-5)] + [-8i+(-7i)] =
(-3-5) + (-8-7)i =
-8 + (-15)i =
-8 - 15i or -1(8+15i).
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.
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.
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