Final answer:
To add or subtract complex numbers, combine the real parts separately and the imaginary parts separately. Then multiply the third complex number by the second complex number using the distributive property. Finally, add the sums together.
Step-by-step explanation:
To add or subtract complex numbers, we combine the real parts and the imaginary parts separately. Let's begin by adding the real parts: 7 - 4 + 2 = 5. Now let's add the imaginary parts: -7i + 5i = -2i. Putting it all together, we have 5 - 2i. This is the sum of the first two complex numbers.
Next, let's multiply the third complex number by the second complex number using the distributive property: (2 + 5i)(-4 + 5i) = -8 - 10i + 20i + 25i^2 = -8 + 15i + 25(-1) = -8 + 15i - 25 = -33 + 15i.
Finally, we can add the sum of the first two complex numbers to the product of the third and second complex numbers: (5 - 2i) + (-33 + 15i) = 5 - 33 + (-2 + 15)i = -28 + 13i. Therefore, the result in standard form is -28 + 13i.