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AmTran_Bus
 one year ago
Really confused all I need is explanation and maybe some steps.
AmTran_Bus
 one year ago
Really confused all I need is explanation and maybe some steps.

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AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Express 6i in the form re^(i theta).

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1@ParthKohli @paki @Nnesha

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1I have the steps. My book says 6i = r cos theta + ir sin theta Then r=6. How?

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1I understand why we use Euler's formula.

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0Yeah well, each complex number is an addition of its "real"part and its "imaginary"part. Whenever you compare two complex numbers, you compare their real and imaginary parts separately. You know what the best way to find out the polarform of a complex number is? Graphing it. dw:1440264084863:dw

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440264204510:dw

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1That is what @phi and @IrishBoy123 said, too, but I still need to understand the actual math.

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Like, I see and think I get the graph. My book has it.

phi
 one year ago
Best ResponseYou've already chosen the best response.2find the magnitude by multiplying by the complex conjugate: \[ (r \cos x + i r \sin x ) (r \cos x i r \sin x )= r^2 \cos^2 x + r^2 \sin^2 x \\ = r^2 ( \cos^2 x + \sin^2 x) \\= r^2 \] and the magnitude is r

phi
 one year ago
Best ResponseYou've already chosen the best response.2thus if you start with 0 + 6 i and find the magnitude, you will get 6 that means r = 6

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1How did you get the 0 in 0+6i?

phi
 one year ago
Best ResponseYou've already chosen the best response.26i is 0 + 6i (if we insist on showing the real component is 0)

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Oh. The z=x+iy formula. Ok.

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1So now I need tan1, which is 6/0?

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.0This is the actual math. If you want to look at it the boring way, here you go:\[\tan \theta=\frac{y}{x} = \frac{\Im(z)}{\Re(z) } = \frac{6}{0}\]\[\Rightarrow \theta = \pi/2\]\[r = \sqrt{x^2 + y^2} = \sqrt{\left(\Re(z)\right)^2 + \left(\Im(z)\right)^2} = 6\]

phi
 one year ago
Best ResponseYou've already chosen the best response.2yes, the angle can be found using inverse tan imag/real

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Thanks! So to express it in that certain form, It must be 6e^(i pi/2)

phi
 one year ago
Best ResponseYou've already chosen the best response.2yes, you are using Euler's \[ e^{ix}= \cos x + i \sin x \]

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440264786581:dw

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Why does my calc say tan 6/0 is undef and yall get pi/2?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0because 6/0 is undefined

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0ask it for \(arctan \frac{6}{0.00000001}\)

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0my calc blows up too. its software just crashes on a singularity, it doesn't ask which function is coming next....

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Can yall help me with one more? 4sqrt(2)i?

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Do I need to multiply it by 4+sqrt(2)i?

phi
 one year ago
Best ResponseYou've already chosen the best response.2you can do sum of squares (then take the square root)

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Ok. Let me get that ans for ya!

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Its just 16+2 right?

phi
 one year ago
Best ResponseYou've already chosen the best response.2yes if you plot it, you see it's pythagoras

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Why does the book say sqrt(16+2) and then 3 sqrt(2)?

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1If I took a picture of the book, would you help me make sense of what its saying?

phi
 one year ago
Best ResponseYou've already chosen the best response.2do you get that the length (distance from the origin) of the point 4 + sqr(2) I is sqr(18)?

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Yes. But this book does not do it that way.

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1It starts under the 6i

phi
 one year ago
Best ResponseYou've already chosen the best response.2they are doing the same thing, but left out the simplifying step. sqrt(16+2) = sqr(18)= sqr(2*9)= sqr(2)*sqr(9) = sqr(2)*3 or \[ 3 \sqrt{2}\]

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Got ya. Thanks. Its just hard for me to see sqrt(16+2), because I thought 4 sqrt(2)i was not under a root.

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1oh you take sqrt to get mag.

phi
 one year ago
Best ResponseYou've already chosen the best response.2if you think pythagoras with sides 4 (along the xaxis ) and sqr(2) (along the y or "i" axis) and c^2 = a^2 + b^2 that should help you remember that x^2 + y^2 is the magnitude squared thus 16+2 = 18 is the mag squared and we want sqr(18) for the actual magnitude.

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Yea, I see where pythagoras helps understand that now.

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0this is from the Gospel of St Mary [Boas, Maths for Physical Sciences] notice how the Argand diagram features prominently

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Wow that is really nice to have. Thanks!

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.1Just solved 3 on my own got em all right

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0you have 30 seconds!
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