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

Question

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

Accepted Answer

Welcome back I am so glad you're here. We are given this expression parentheses four minus three I. And those parentheses minus parentheses seven plus six I. And those parentheses minus new parentheses minus eight plus I. Or negative eight plus I. And we are to perform this subtraction and then use Standard form to write our final answer. We recall from previous lessons. That standard form is going to be in the format A plus B. Y. Where A is all those regular real numbers and then B. I. Is all of those numbers attached to imaginary numbers. So first step here is that we have these negatives in front of our 2nd and 3rd set of parentheses that's like a negative one squished up against that needs to be distributed to the terms on the inside of the parentheses. So let's bring down our first set of parentheses. That one doesn't have a negative in front of it. So we can actually drop those parentheses that's just 4 -3. I now let's distribute our negatives so negative one times seven is going to be a minus seven. Negative one times six I is going to be minus six. I. And for this third set of parentheses negative one times negative eight is going to be plus eight. Negative one times I is going to be minus I. Now we just have to combine our real terms and our imaginary terms let's start with the real ones four negative seven and plus eight. Four minus seven is minus three plus eight is going to be a plus five. So positive five. Now let's combine these imaginary ones negative three I. Negative six I and minus I. So we take negative three I minus six I. That's minus nine I minus one more. I gives us negative 10 I. And there is our answer. In its standard form we look at our answer choices for 5 -10 I that matches with answer choice C. Well done, we'll catch you on the next one.

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

Key Concepts

Complex Numbers and Standard Form

Addition and Subtraction of Complex Numbers

Distributive Property and Handling Negative Signs

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