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IrishBoy123
 one year ago
find
IrishBoy123
 one year ago
find

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IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3\[\left \dfrac{2e^{i \theta}  i}{ie^{i \theta}+2} \right\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2we may use the property \(\left\dfrac{z_1}{z_2}\right=\dfrac{z_1}{z_2}\) : \[\left \dfrac{2e^{i \theta}  i}{ie^{i \theta}+2} \right = \dfrac{2\cos\theta + i(2\sin\theta1)}{2\sin\theta+i\cos\theta}=1\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440667852028:dw

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3dw:1440668386653:dw

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2oh right, i got that second circle to the wrong scale.

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440668618259:dw

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3my little brain is whirring here so for the denominator you take the unit circle and shift it right because of the \(+2\) and the fact it is also \(\times i \) only changes the sin and the cos round and does not change the actual number itself?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2the i is just a π/2 rotation

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440668948392:dw

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440669146594:dw

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3i'm miles behind you on the triangles but i can see where you came out, therefore i "should" be able to figure it out in a while. my first instinct is always to draw things so i will study these carefully. i am thinking of sitting through these https://www.youtube.com/watch?v=bAJsyojpekI&list=PLkfmuPOLLntiM_HjGFSUTyINMfgVszca&index=1 i love this stuff but it's been so long and i'm trying to find my way around. drawing/seeing it for me is really important. so thanks!

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3silly question but do i need to factor in the \(\pi/2\) phase shift before comparing the numbers?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440669675928:dw

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3\[\left \frac{2e^{iθ}−i}{e^{i(θ+\frac{\pi}{2})}+2} \right\] dw:1440670064162:dw yeah, i think i'm getting there my crap drawing is for the specialised case \(\theta = 0\)

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3dw:1440670317848:dw and \(\theta = \frac{\pi}{2} \)!!

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3dw:1440670437299:dw \(\theta = \pi\)

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3i can see! it's a bit blurry but i can see! thank you both

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440671876306:dw