Find each sum or difference. Write answers in standard form. (...

Question

Find each sum or difference. Write answers in standard form. (-4-i) - (2+3i) + (-4+5i)

Accepted Answer

Welcome back I am so glad you're here. We are given this expression. We have parentheses -3 -2. I. And those parentheses minus new parentheses four plus nine. I end those parentheses plus new parentheses negative seven plus eight. I were to perform the addition and the subtraction that are given in the expression. And to use standard form to write the final answer, recalling from previous lessons. That standard form when we're dealing with these eyes is going to be A plus B. I. Meaning that all of the regular numbers, the A's come first and then the ones that are attached to an eye, the B. I's come second. So we've got a couple of things to do here. We see that our parentheses here have a subtraction sign in front of them. That is like a -1 that needs to be distributed to the two terms on the inside. The other two sets of parentheses don't have any subtraction in front of them so we can just bring them down dropping their parentheses. So we have negative three minus two. I now let's distribute that negative one. So negative one times four is going to be minus four, negative one times nine I is going to be a minus nine I. And then bringing down plus that will be a negative seven and a plus eight. I now we just need to combine like terms. So let's combine all of the constant terms that don't have any eyes attached to them. So negative three minus four. That's negative seven minus seven more. That's going to be negative 14. And now let's combine all the terms that have the eyes attached to those be eyes. So negative two I negative nine I and plus eight I negative two I minus nine. Eyes negative 11 I plus eight I is going to be minus three I. So here is our answer. It is in standard form we look at our answer choices for -14 -3 I and that matches with answer choice. A well done. We'll catch you on the next one.

Find each sum or difference. Write answers in standard form. (-4-i) - (2+3i) + (-4+5i)

Key Concepts

Complex Numbers and Standard Form

Addition and Subtraction of Complex Numbers

Distributive Property and Grouping Like Terms

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