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

Question

In Exercises 1–8, add or subtract as indicated and write the result in standard form.

6 - (- 5 + 4i) - (- 13 - i)

Accepted Answer

Hello Today we're going to be rewriting the complex expression in standard form. So the complex expression given to us is the quantity negative five I minus four plus. The quantity three minus eight. I plus five. Now notice how this expression has a sum of three quantities. That means you can go ahead and rewrite the entire expression without the need of the parentheses. So doing so is going to give us negative five. I minus four plus three minus eight. I plus five. And in order to simplify this, we're just gonna go ahead and combine the like terms together. While any term involving I can be added together and all the constant values can be added together as well. So negative eight I minus five. I is going to give us negative 13. I. And negative four plus three plus five is going to give us positive four. So this is the simplified version of this expression. But keep in mind that the standard form is always in the form of A plus or minus B. I. Where the imaginary number goes after the real number. So reordering this with the real number in front is going to give us the quantity four minus 13 I. And this is going to be the standard version of our given complex expression. And that means that the answer to this problem is going to be d. So I hope this video helps you in understanding how to simplify this complex expression and I'll go ahead and see you all in the next video

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

Standard Form of Complex Numbers

Distributive Property

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