Final answer:
To add complex numbers, combine the real parts and the imaginary parts separately. The sum of (-4 - 7i) and (5 - 7i) is performed by adding (-4 + 5) and (-7i - 7i) respectively, resulting in a final answer of 1 - 14i.
Step-by-step explanation:
To understand how to add complex numbers, like (-4 - 7i) + (5 - 7i), you simply add the real parts and the imaginary parts separately. In this case, add the real numbers -4 and 5 together, and separately add the imaginary numbers -7i and -7i together. Remember, when two positive numbers are added, the result has a +ve sign, when two negative numbers are added, the result has a -ve sign, and when numbers with opposite signs are added, subtract the smaller number from the larger one, giving your result the sign of the larger number.
Thus, for the real parts: -4 + 5 = 1, since you are adding a negative number to a positive number, which is similar to subtraction. For the imaginary parts: -7i + (-7i) = -14i, since adding two numbers with the same sign retains that sign. Combine both and you get the simple addition: 1 - 14i.
Steps for Addition of Complex Numbers:
- Add the real parts: -4 + 5 = 1.
- Add the imaginary parts: -7i + (-7i) = -14i.
- Combine the results from step 1 and 2 to form the new complex number: 1 - 14i.
When subtracting complex numbers, you would follow similar steps but take care to change the sign on the imaginary part being subtracted before carrying out the operation, much like subtracting scalars.