In Exercises 1–8, add or subtract as indicated and write the r...

Question

In Exercises 1–8, add or subtract as indicated and write the result in standard form. 6 − (−5 + 4i) − (−13 − i)

Accepted Answer

Welcome back. Everyone. In this problem, we want to compute 11 minus negative two plus six, I minus negative 17 minus two. I. And we want to express our answer in the standard form for complex numbers. For our answer choices A is 30 minus eight I B is 30 minus four. IC is negative four minus eight I and D is 26 plus eight. I no, we want to write or answer in standard form. That means after we've computed, then we want to write it in the form because recall that the standard form for complex numbers is A plus B I where A is the real part and B is the imaginary part. So let's go ahead and simplify and to do that. Now 11 minus negative two becomes plus two and minus positive six, I becomes minus six. I likewise, when we subtract negative 17, that becomes plus 17 and we subtract negative two I, it becomes plus two. I now we can combine our like terms. Notice that 11 2 and 17 are alike while negative six I and two I are alike. So by combining those 11 plus two is 13 plus 17. Equals 30 negative six I plus two. I is minus four. I, no, we can't simplify it any further. So the question is, is it in standard form? Well, yes, it is. Our real part A came first and then our imaginary part negative four came second. So no, it's in standard form. And when we look at our answer choices that would have been answer choice B thanks a lot for watching everyone. I hope this video helped.

In Exercises 1–8, add or subtract as indicated and write the result in standard form. 6 − (−5 + 4i) − (−13 − i)

Key Concepts

Complex Numbers and Standard Form

Addition and Subtraction of Complex Numbers

Handling Negative Signs and Parentheses

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