5

Convert the complex number from polar to rectangular form. 2 = 5 cis...

Question

Convert the complex number from polar to rectangular form. 2 = 5 cis

Convert the complex number from polar to rectangular form. 2 = 5 cis



Answers

Convert the complex number from polar to rectangular form: $z=5 \operatorname{cis}\left(\frac{2 \pi}{3}\right)$.

So in this question, were given the complex number seven times says off 25 degrees in the order form, and we were asked to convert it to standards Rectangular recording. This, um, so I wrote the former national to right here way. Have a complex number. Are time sensitive data than access art. I've to go China, Tita. And why is r times to sign of Tina? And so in our case, we have our eagle seven Did, uh, given in degrees, uh, 25 degrees. And now this is not a very nice angle, too, to calculus, although it looks very nice, but on the go sign off 25 degrees. Isn't that a nice number? Um, it is actually zero points. Nine 06 and one somewhere. Numbers on the sign off. 25 degrees. Yes. Um, zero points for to three. We'll just use the 1st 3 digits. Uh, so using this information, we find that X iss seven times. Go shine. 25 25 degrees. Um, which is seven times 0.9 or six. This is 6.34 two pens. Why is seven times signed off 25 degrees and says the Sinus. Gerald points for 23 This is to find 961 And so we can use this to write our number in Earth. Angular ordinance, Our numbers. Seven assists. 25 degrees s. So what is this? Six points 34 through. Bless. Why two points? 96 One time I This is everything in order form over another.

So in this question, we were given the complex number, um, square root of dude. I'm cysts off 100 degrees in order form and were asked to convert it to rectangular form. Onda foreman us to do this. I wrote your own the rights. Um, in our case, we have homogeneous are it's discovered of two. This is first digit of this are one point for one, and ah, I most ada is 100 degrees. So we need to calculate the coastline in the sign off this angle, which, um or not. Nice numbers. Meth. Uh, we can calculate them of through the 1st 3 digits. The coastline of 100 degrees. Yes. Minus 0.174 and sign 100 degrees. It is, um, Cheryl wants. I'm it's five. And so we can use this to, uh, calculate x and Y for our rectangular coordinates. So X is, um, describe. It is to times you co sign off one of degrees, and this is the first digits off these numbers are monk went for one times minus. Is there a 0.174 And this gifts minus zero points. Two for us now you're the same for why here? We have scours too. Times sign off 100 degrees. The first edges of this for one points for one times zero points. Nine, it's five. And here we gots 1.3 nine. And so, if we use this to write our number in, uh, rectangular coordinates, then we see that our number skirt of two things I just wanted degrees equal to minus zero points threw for five plus one points. 39 times I This is different. Thanking her for our number.

In this question were given Ah, uh, complex number in boner form. Uh, through times, assists by or three. And we were asked to write. It's in Northanger for him. So uniform X plus y times. I, um that for me not to do this I wrote on the right here. If we have a number our time successive Tita than Xs are Pepsico's gonna Tita and Wise our time to sign of tea down. And so in this guy's we have ours, too, And, um that I iss by over tree Lucky I ever threw you to comment. Uh, the common angle. So we know the values of the co sign and the sign. No. Did it go sign? Well, by over three. This 1/2 And the sign by over three is the scarlet of three divided by two. And so we find that X is are times because I'm off by over three. This is, uh do that. What? Half as we just clean. It s so excess one. And why? Which is our plans to sign? Fly over three. This is two times describe it. A three over to s. Oh, this is just scrabbled of three. So combining this we find that our number two sis whatever works for you invited in our standard reform ISS one bless discovered three. I'm trying.

Were given a complex number, and Cartesian foreign were asked to write it. In polar form, Cartesian number is two minus five I to convert to polar form. We want to calculate or in theater Yeah, that or is thes square roots of four plus 25 which is a square 29. And that data satisfies the inverse tangent of data equals negative five halves. Since this is negative, this is going to give us a negative value. Stato. If we want to choose a positive value of data, we'll want data to be equal to 3 60 degrees, plus the inverse tangent of negative five halves, which is the same as minus the inverse tangent of five halves. And this is approximately equal to 291 0.8 degrees. And so in polar form, the number has the form are co sign of data plus I or sign of data. And this is simply an approximation


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