In Exercises 48–57, perform the indicated operations and write th...

Question

In Exercises 48–57, perform the indicated operations and write the result in standard form. (7-i)(2+3i)

Accepted Answer

Hello. Today we're going to be simplifying a complex number and writing it in standard form. So the operation given to us is eight plus I Times five Plus 2. I now in order to start simplifying this, we're going to go ahead and foil both of these quantities together. So for foil we're gonna multiply eight and five together. That's going to give us 40. Then we're gonna multiply 8-2 I and that's going to give us 16 next we're gonna multiply I and that's going to give us five I and finally we're gonna multiply eye to to eye and that's gonna give us to I squared. Now recall that I squared is equal to negative one. That means that we can go ahead and rewrite to I squared as two I I'm sorry not to I two times negative one. Now let's go ahead and simplify this two times negative one is just going to give us negative two and 16 plus five I is going to give us 21 I. And finally we can go ahead and combine 40 and negative two And that's gonna give us 38. So we're left with 38 plus 21. I now recall that the standard form of a complex number is A plus or minus B. I. Plus or minus because this quantity can either be positive or negative. A represents a real number and B represents the imaginary number and this matches the standard form. So this is going to be our solution. This also means that the solution to this problem is going to be a So I hope this video helps you understand what I squared is and writing a complex number in standard form, and I'll go ahead and see you all in the next video.

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