Find zw. Leave your answer in polar form.z = 2 (cos(π)/(9) +...

Name: Find zw. Leave your answer in polar form.z = 2 (cos(π)/(9) + i sin(π)/(9))w = 7 (cos(π)/(11) + i sin(π)/(11))
Uploaded: 2022-08-13T02:51:31-08:00
Duration: 7 min 7 s
Channel: Darryl Burns
Description: Find zw. Leave your answer in polar form.z = 2 (cos(π)/(9) + i sin(π)/(9))w = 7 (cos(π)/(11) + i sin(π)/(11))

Transcript

00:01 Euler's equation is an excellent way to write angles or what's called parameterized coordinates.

00:08 Oiler's equation is written like this.

00:11 So the radius times e raised to the imaginary number i times the angle can be written as the radius times cosine of the angle plus i times sine of the angle.

00:35 So this is euler's equation.

00:41 And this is going to help us figure things out when we have to transfer between different types of coordinates.

00:46 For example, let's say that we had a function, z, call it z.

00:51 And let's say that z was equal to six times cosine of pi over 10 plus i sine of pi over 10.

01:06 Let's also do another function, w.

01:08 Let's say w is 6.

01:10 Six times cosine of let's say pi over 11 and we're going to add to that i sign of the same angle pie over 11.

01:23 So it's important the angle needs to be the same so that we can rewrite them using oilless formula.

01:30 All right so let's pick up the parts.

01:31 This is the radius and these two parts represent your angle theta.

01:40 So rewriting or formula we have 6 e to the i and the ankle is pi over 10 so oilless formula allows you to condense this equation into just an exponential or a an exponential expression okay now e is actually oil is number that e is approximately equal to 2 .71828 and so on it's repeating like pi or not repeating but rather continuously adding unique numbers with no particular order like pi.

02:19 It's a transcendental number.

02:21 Now, w, we see that 6 cosine of pi over 11 plus i sign of pi over 11.

02:27 We can condense that in oilers equation as 6 e to the i pi over 11.

02:35 So how would this work with some operations? let's try some operations.

02:39 So let's say that we wanted to find z times w.

02:43 Well, z times w is just going to be what z is.

02:46 Which is in this case we can write it as the exponential form be easier to multiply.

02:52 That'll be 6e to the i pi over 10 times w, which is 6e to the i pi over 11.

03:07 All right, so what is this equal? well, 6 times 6, the numbers is going to give us 36...

Question

Find zw. Leave your answer in polar form.\ z = 2 \left(\cos \frac{\pi}{9} + i \sin \frac{\pi}{9}\right)\ w = 7 \left(\cos \frac{\pi}{11} + i \sin \frac{\pi}{11}\right)

Question

Find zw. Leave your answer in polar form.\ z = 2 \left(\cos \frac{\pi}{9} + i \sin \frac{\pi}{9}\right)\ w = 7 \left(\cos \frac{\pi}{11} + i \sin \frac{\pi}{11}\right)

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