Question

Need help studying Polar/Cartesian forms and Trigonometric form

Answer 1

https://gyazo.com/da262a849072b70cb53c18b16f567e41

Answer 2

I have a huge test on this stuff tomorrow and for some reason I can't get _anything_ to work out

Answer 3

The rectangular coordinates can be found by the formula:
\[x=r*cos(a)\]
\[y=r*sin(a)\]
Where r is the length and is the angle

Answer 4

so if I do x = 7 * cos(2pi/3)

Answer 5

Yes, then you have the rectangular x coordinate

Answer 6

7* -1/2 = -7/2

Answer 7

Yes

Answer 8

what about https://gyazo.com/9988ae7493b7d63ee2f5677115e79914

Answer 9

?

Answer 10

@SamsungFanBoy

Answer 11

@Tommynaiter https://gyazo.com/da262a849072b70cb53c18b16f567e41

Answer 12

@AlexandervonHumboldt2

Answer 13

@imqwerty

Answer 14

I feel like I think I know what I'm doing but the way I wanna do it feels ridiculously long

Answer 15

I think I linked the wrong gyazo, this is the one that's giving me problems

Answer 16

https://gyazo.com/14ef47a342447b44686220a3e5617aa0

Answer 17

Got anything?

Answer 18

@pooja195

Answer 19

@thomaster

Answer 20

https://gyazo.com/14ef47a342447b44686220a3e5617aa0

Answer 21

okay we can write any complex number like Z=a+ib in this form-\[Z=r(\cos \theta +i \sin \theta)\]where\[r=\sqrt{a^2+b^2}\]

Answer 22

ok did this help?
lol

Answer 23

To a point, I already knew that but I'm stuck on adding the angles to get the final form

Answer 24

Like, I have 5pi/6 and pi/4 if I remember correctly but I can't get them to equal 23pi/12 or pi/12

Answer 25

I think I did theta wrong

Answer 26

oh ok ima tell that part :)

Answer 27

https://gyazo.com/584527bec146ee0d4b47ea4b4609841c
also for this I know that

I do 2^3(cos(15*3)+isin(15*3)) but that gives me 8(cos45+isin45)
8(sqrt2/2 + (sqrt2/2)i)
4sqrt2 + 4sqrti
did I do that right?

Answer 28

ok \[\cos \theta=\frac{ a }{ \sqrt{a^2 +b^2} }\]
\[\sin \theta=\frac{ b }{\sqrt{a^2+b^2 }}\]

so here we shuld take the principle value of θ

\[Z=r[\cos(2n \pi +\theta)+i \sin(2n \pi+ \theta)]\]

where n is an integer
try doing it now

Answer 29

I think the answer is C

Answer 30

But I did it differently, I converted each equation separately then divided r and subtracted the angles

Answer 31

I mean
I multiplied r1 with r2 and added the angles

Answer 32

https://gyazo.com/62881a9809a919bc9db0e743d1a7b05a