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Write the expression in rectangular form x +y and in exponential form ( 2 (0 [A(cos isin '4]' The rectangular form of the given expression is and Ihe expo...

Question

Write the expression in rectangular form x +y and in exponential form ( 2 (0 [A(cos isin '4]' The rectangular form of the given expression is and Ihe exponential form of the (Simplily your answers. Type exaci given expression Is answers; using K as needed Use integers or fractions for any numbers In Ihe expressions )

Write the expression in rectangular form x +y and in exponential form ( 2 (0 [A(cos isin '4]' The rectangular form of the given expression is and Ihe exponential form of the (Simplily your answers. Type exaci given expression Is answers; using K as needed Use integers or fractions for any numbers In Ihe expressions )



Answers

Find each power. Write the answer in rectangular form. Do not use a calculator. $$(2-2 i \sqrt{3})^{4}$$

I guess so. We want to write the following expression in rectangular form, so it's not here. We have this intricate form raised to the power of eight. So let's use the M zero. So here we can rewrite this. Let's no thoughts. Um, we don't have or we have no coefficient in front of this term. That means our our value is one on our end. Value is eight. So we have our to the power of eights. That's once you pair of eights and then we have co sign of eight times pi over four and then plus I sine of eight. And in pi over four. So this is going to give us co sign of to pocket. Plus I sine of two pi. So evaluating this, we know that co sign of two pi that's equal to one and sign of two pi Israel. So we see that we're left with a one

We have to find the fourth power of a given complex numbers. You know that according to the movies there if a complex number is it is and it's trigonometry form artist data. It's in the power is given by the address to a music where two are raised to and induces and rita. So here we can use this form life we convert the given number and do it techno metric form. So our number is equal to two minus 2 3. I it's more or less is equal to Saratov two square plus -23 or square that is equal to four. And the argument they take will to john universe be by a That is equal to 16 or it is legal to 300 degrees. No I can't either. Given number is four new six 300 and we have to find it's for power that is for 6 300 is to four that is equal to for rest of or induces foreign New 300 that is equal to 2 56 Hindu of course. 200 plus I signed 1002 100. And we can convert this in due An angle less than 316 that is equal to 256. In the course 1 20 plus I side 1 20. We have to convert it in the standard form so we can substitute the values of course inside functions that is cause one twenty's minus one by two because I into sign when 20 days route three by two That is equal to -128. Yes 128 into room three I This is the for the power of given complex numbered.

Okay, so we would sue Finder falling power. So it's notice that we have or complex number and rectal you if one. So if you get rid of this power, we're gonna need to use the M zone, but that requires that we have our conflicts number in trig form. So let's stop everybody in this insurance form to have our is equal to the square roots of negative square root of two over its use gray plus the square root of 2/2 to the power to She just gives us that we have to over four, which is one half plus one house. So we see that we get the square root of one half plus one half, which is one. Now, let's also find data data Is tangent inverse of or be value over are a value. So that's detentions inverse of one negative one. It's a tangent. Intrusively one is negative. 45 threes. I'm gonna add 362 up to get that between zero and 360. So this is actually 215 degrees. Okay, so, no, we can use the m zoom, so this gives us that we have, um, or our value to the power of and and then we assists of n time stream 15 degrees. So this gives us a We have co sign of four times 3 15 That's 1000 and 60 1000, 260 degrees. Plus I'm sign of the same degrees. Now let's evaluate this. So co sign of 1 to 6 year old, that's going to be negative. One inside of that. So you have this, Errol. So we see that we're left with this. Ah, negative one.

So in this question we have been given to find each power and we need to write each answer and rectangular form. Now the given question is two minus to Biota. Room three. Hold the power for no. Therefore we can rewrite this as equal to two. Window 1 -1 order up three. Go to the bottom. Sure. No this can be rewritten as To to the Border four and 2 1 -6 Room three holding the power of four. No again this can be rewritten since two to the power of foreign to two times off half minus iota route three by two or to the part of. Therefore this can be rewritten as through to the power of it into half minus iota three by Hold the Bottom four. Okay so now therefore this is nothing but it will do 2 to the power of eight into 16. So therefore hold the power for no we can read it. This is equal to the power of aid into six off 300 degrees or to the border for therefore this is what we will do To the power of eight which is equal to 256. Hold into now from the university here in another sense of three to hold, the power of N is equal to six of end times Theta. Therefore, by substituting the value of theta as 300 degrees and N as equal to four, We will get this has 256 and two Says all four into 300°,, which is 1200°.. Well, we can evaluate the value of six or 1200 degrees, has cost 1200 degrees, precise and 1200 degrees and therefore we will obtain the final dessert is equal to -128. Place iota 1 28. So this is thank you french. I hope you like the video.


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