Adding and Subtracting Complex Numbers - Problem 1

Adding and subtracting complex numbers. So behind me I have a problem that has a bunch of different square roots, and in order to simplify this up the fist thing we have to do is simplify each component individually.

Looking at this, square root of 64 we know that, that’s 8, square root of -36, we can break that up into the square root of 36 and the square root of -1, square root of 36 is 6, square root of -1 is i. So this then ends up as plus 6i. There’s our first term, minus square root of 9 which is 3, and splitting up our square root of -4, this becomes the square root of 4 times the square root of -1. Square root of 4 is 2 and our square root of -1 becomes a i.

Once we have simplified each of our square roots we now just add and subtract, combining like terms. First thing I would do is make sure this negative sign gets distributed through everything in the second term. We end up with 8 plus 6i minus 3, minus and minus this becomes plus 2i. And then just combine the like terms. So we have 8 minus 3 becomes 5 and 6i plus 2i becomes 8i.

Simplifying, adding and subtracting complex numbers, first rewrite them getting rid of as much square root as you can and then just combine like terms till you end up with a complex number, you have a real component and an imaginary component.