In Exercises 1–3, perform the indicated operations and write the ...

Question

In Exercises 1–3, perform the indicated operations and write the result in standard form.(6 − 7i)(2 + 5i)

Accepted Answer

Welcome back. Everyone. In this problem, we want to simplify the expression three minus nine. I multiplied by one plus eight I and express our answer in standard form for our answer choices. A is negative 75 plus 15. IB is 75 plus 15. IC is 33 plus 69 I and D is negative 33 plus 69. I. Now what do we already know? We're multiplying complex numbers. So we can go ahead and multiply by multiplying each term by the other terms in the other bracket. So if we do that, this would equal three multiplied by one, which is three and three multiplied by eight I which is 24. I next negative nine, I multiplied by one is negative nine I and negative nine, I multiplied by eight. I is negative 72 I squared. Now, before we continue recall that for complex numbers I squared equals negative one. So we can rewrite this as three plus 24 I minus nine, I minus 72 multiplied by negative one. We can simplify 24 I minus nine I that gives us 15 I and negative 72 minus one. That's positive 72 we can simplify even further because three plus 72 is 75 which means that our final answer would be 75 plus 50 I, which would have been answer choice. B Thanks a lot for watching. I hope this video helped.

Struggling with Trigonometry?

In Exercises 1–3, perform the indicated operations and write the result in standard form.(6 − 7i)(2 + 5i)

Watch next

Graphing Complex Numbers practice set