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Chapter 6

Test Yourself

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01:39

Divide the complex numbers…

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Find real numbers $a$ and …

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Simplify the complex numbe…

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Simplify. Write answers in…

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Find the product of the gi…

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Write each complex number …

can. So this says, if the product of two complex numbers April's for I and nine Minutes B I is a real number. And if a is equal to six, what is the value of B? So first of all, if a is equal to six, let's go out and plug that in just so that we could make a little bit easier for Russell's on. Then it says the product, which is he word for multiply. So then we're going to multiply this and nine minus B I. So let's go and try expanding that. So we're going to just go ahead and foil that, which means it's going to be six times nine, fifty four, six times negative eyes negative six b I and then four aye times eyes going to be close. Thirty six I and then four I times negative b I was gonna be minus for B. I squared, but we know that I squared is just negative one. So this right here could become close for B. So this is going to become riel. So we've got a real component here, a real component here, and so these are our only imaginary components that we have to figure out a way to get that to become real. So the only way for this imaginary components become really is if we can cancel it up, meaning that this thirty six I and this native six b I are equal to each other. And so one day are added one negative component and one positive component they're going to cancel out. So we know that this negative six b should equal thirty six in order for them to cancel out. So then we can just go ahead and divide by negative six on both sides to get that B is equal to negative six. And so Ah, well, I guess we're just going toe have this component right here. So I'm going to make everything positive. So be should be six. So, Caesar answer. So just to put it back in, what's going on? Checks of fifty four minus six times six is thirty six. I class thirty six, I minus four times six is twenty four. Okay, so then this becomes plus twenty four got fifty four, and this component right here at this negative thirty six I in this positive thirty since I were just the same thing except one is negative and one is positive. So they're going to cancel out, so we know that this whole thing becomes real.

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Divide the complex numbers. Write the answer in the form $a+b i$.$$\frac…

Find real numbers $a$ and $b$ such that the equation is true.$$a+b i=-9+…

Simplify the complex numbers. Write the answer in the form $a+b i$.$$\fr…

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

Find the product of the given complex number and its conjugate.

$$

Write each complex number in the standard form $a+b i$ and clearly identify …

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