In Exercises 1–10, perform the indicated operations and write ...

Question

In Exercises 1–10, perform the indicated operations and write the result in standard form. (7 + 8i)(7 − 8i)

Accepted Answer

Welcome back. Everyone. In this problem, we want to simplify the expression 11 plus 17, I multiplied by 11 minus 17 I and express our answer in standard form that is writing it in the form A plus B I where A is a real number and B is an imaginary number for our answer choices A is 410 B is 121 minus 289. IC is 289 minus I and D is negative 168. Now, first of all, what do we know? Well, we, we are multiplying two complex numbers here but if you look at them very carefully, it jogs your memory of a little algebra a bit because notice that this is the difference of two squares and recall that the difference of two squares tells us that if we are multiplying two values where their difference is the either plus sign or the negative sign, then it will be equal to the square of one of those values minus the square of the other, the difference of the two squares. So we can apply that idea here because we have 11, which would technically be X and 17 I, which would have been Y. So that means we can rewrite 11 plus 17. I multiplied by 11 minus 17, I as 11 squared minus 17, I squared. No, 11 squared is 121 and 17, I squared is 289. So that's 121 minus 289 I squared because we've also squared I no recall another important property recall that I squared equals negative one for complex numbers. So that means we can rewrite our expression as 121 minus multiplied by negative one. This now becomes 121 plus which is equal to 410. Therefore, our answer is 410 which is answer choice. A thanks a lot for watching everyone. I hope this video helped.

In Exercises 1–10, perform the indicated operations and write the result in standard form. (7 + 8i)(7 − 8i)

Key Concepts

Complex Numbers and Standard Form

Multiplication of Complex Conjugates

Use of the Imaginary Unit i

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