in-35-43-write-each-number-in-simplest-form-3-i2-i3

Question

In $35-43,$ write each number in simplest form.
$$
3 i+2 i^{3}
$$

Martha Richards · Accepted Answer

Okay. This problem here with God and oops Don&#x27;t do that guy. Let&#x27;s hear we&#x27;ve got and I plus an I squared plus and I cubed plus an eye to the fourth. So here we have this eye that doesn&#x27;t go anywhere And then we know that I squared is a negative one And then we know that I squared was negative one and then another I would be a negative I And then we have this ID of the fourth, which we know is one because it&#x27;s I square toe a negative one times eight negative one, which is one. So you see here that all of these guys cancel out and we&#x27;re left with zero.

Martha Richards · Answer

Okay. Our next problems here are asking you to put these questions here or these imaginary numbers into their lowest or their most reduced form. And so what we know is is that when we have an I times and I right, we have that&#x27;s a negative square root of one times of negative square root of one. So that&#x27;s equal to negative one, right? And then we can use that to deuce, deduce other things. And they went out through a whole thing in the book here, so I&#x27;m not gonna do all that. But what you know here is that an I squared is a negative one. So here I have five times a negative one and then plus a two and this eye to the fourth. If I have I squared here. But I have it twice because remember, if I have I squared times I square. That&#x27;s the same thing is I to the fourth. And so what that means is is that we know that I squared was a negative one. So this is negative one times a negative one, which is one and so this ID the fourth is one so two times a one. So this is negative five plus two, which is equal to negative three

Martha Richards · Answer

Okay, So our next problem here that we&#x27;re gonna put into simplest form as four I plus five I to the eighth plus six i to the third and then plus to I to the fourth. So here this four eyes just gonna stay as is this eye to the eighth. We know that I did the fourth some a little bit too high up there. Either The fourth time&#x27;s eye to the fourth would be I the eighth. And I did The fourth is just one. So this is equal to one. So then I have a plus five this IDed the third we know we know that I squared was a negative one. And then one more I So that&#x27;s a negative. I So I get a negative six i and then this ID of the fourth. We know that that&#x27;s one. So what? Two times one is just too. So here I see that I can combine these guys and then I can combine these two. And so I have a five and a positive too, which is seven. And then afore I minus the six. I is minus two. I

Martha Richards · Answer

Okay. Next problem here that they&#x27;re asking us to reduce is I to the 52 out of the five plus seven I to the seven. So we knew that I to the fourth was one. So out of the fourth time&#x27;s another I that would be I to the fifth is equal to ay. And so here this side of the fifth just becomes I And then this IDed the seventh, while we know that I to the fourth was one. And then times are I too. We knew I squared right with negative one and then one more eye. Right? So that&#x27;s 4567 Right? Because you add those exponents when you multiply them together. So we know that this is a one. This is a negative one, and this is I So this is equal to a negative, I So here you get a negative I and so this becomes too I minus a seven I. So that is equal to a negative five. I

Amy Jiang · Answer

Okay, so let&#x27;s start using our product rule on your Susan. 32 pair of 1/2 plus 3/2. What Article two for over two, which is two. So that&#x27;s three t part two, which is equal tonight.

Problem

In $35-43,$ write each number in simplest form. …

Problem 35 Easy Difficulty

In $35-43,$ write each number in simplest form.
$$
3 i+2 i^{3}
$$

Answer

$\dot{z}$

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Absolute Value - Example 1

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