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. (3 − 4i)²

Accepted Answer

Hello, everyone. We are asked which of the following expressions is equivalent to the complex number 13 minus two I squared. A 169 minus four I B 173 plus 52 I C 165 minus 52 I D 162 minus 58. I starting by rewriting my expression. So we have 13 minus two I which is in parentheses squared, we can use the same pattern that we used when scoring a binomial, which if you recall means we square the first term. So 13 squared and then we square the last term. So negative two, I, I'm putting that in parentheses squared. And then we're gonna add the product of the two terms of the binomial. So negative two, I multiplied by 13 I oh not I just 13. And then we double that. So we multiply it again by two. So now I'm gonna do out my multiplication. 13 squared is negative two I squared would be plus four I squared and then two multiplied by negative two, I multiplied by 13. Let's see that would give me negative 52. I and I put that in parentheses just because I had double signs, I'm going to rewrite this with I squared substituted as negative one because I squared does equal negative one. So 169 plus four multiplied by negative one minus 52 I four multiplied by negative one is negative four. So 169 plus negative four would be 165 and then minus 52. I because there's nothing else to combine that with. And that is our equivalent expression and answer choice. C 165 minus 52. I have a nice day.

In Exercises 1–10, perform the indicated operations and write the result in standard form. (3 − 4i)²

Key Concepts

Complex Numbers and Standard Form

Binomial Expansion (Squaring a Complex Number)

Properties of the Imaginary Unit i

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