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Chapter 6

Test Yourself

Chapter

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02:19

Multiply and write your an…

02:46

02:16

Perform the addition or su…

01:27

Express $\frac{-2+i}{4+2 i…

02:34

Perform the indicated oper…

00:26

Add or subtract as indicat…

00:34

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Simplify. Write answers in…

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00:49

Okay, So this one says, if eyes equal to the square root of negative one and a plus b I the quantity times the quantity one plus I is acquitted. Three plus five I then a plus b I is equal to what? So Because we have this situation right here, we know that this is something that we have to foil. So that means foil. So that means you have to do the first inside outside inside and last. So if we were to do that, then we would get a because eight times one is a then may I? Because eight times I it's just a tie. Then be I terms one s p i. And then be I times I miss Bea. I squared because I is equal to the square root of negative one. If we square it, that's the same thing. I just negative one because this square on the square root are opposite. So they basically canceled out. So we know that I squared is extra just negative one. So if we were to replace this, I squared right here with the negative one, then we'd have a place A i plus B I because be times negative one which is the same thing as a plus a I plus p I minus B. So then we know that this equation that we've expanded is the same thing as a three plus five I. So then we can essentially take the rial components and the the imaginary components and separate them. So here and here are our real components because those are the ones that don't have eyes touch them. So we know that this minus thiss should equal this so we can say a minus B is equal to three. So then we're going to look at the imaginary components, which is the A I and the B I. So that must equal the five I. So then that means a plus B must equal that five. Okay, so now we just have a system of equations because we have two equations with two unknowns. So we can just go ahead and solve for that so that I think the easiest way to software this one would just be to add the two equations. And once we add that will have April's age too, eh? And then negative B plus B just cancels each other out to that zero and then three plus five eight. So now the equation that we have is to a is equal to eight. So then, in order to isolate the A weakened divide both sides by two, then we'LL have a is equal to four. So now we found what is. We still have to find what B is. So in order to do that, we can plug it back in to either one of our equations. So let's go ahead and pick the first one. The first one said a minus B is equal to three, so four minus B is equal to three. That must mean that we can subtract four from both sides, so P is equal to agree minus four, which is negative one and then multiply both sides by negative one, which means big is equal to one. So we know that a is equal to four and B is equal to one so that if we plug it back into our A plus B I format, then we would have four plus one eye, which is just I. So we know that he has to be our correct answer. So especially in this question, the most important thing is to separate the real components and imaginary components and make equations out of them and then saw for that system of equations.

Multiply and write your answer in $a+b i$ form.a. $(-3+2 i)(2+3 i)$ b. $…

Multiply and write your answer in $a+b i$ form.a. $(-4-2 i)(3+2 i)$ b. $…

Perform the addition or subtraction. Write the result in $a+b i$ form.a.…

Express $\frac{-2+i}{4+2 i}$ in the form $a+b i$

Perform the indicated operations and write the result in the form $a+b i$.

Add or subtract as indicated. Write your answers in the form $a+b i$$$

Simplify. Write answers in the form $a+b i,$ where a and b are real numbers.…

Add or subtract as indicated. Write the result in the form $a+b i$.$$(3+…

Perform the indicated operations. Write the answer in the form $a+b i$.$…