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iop360
 3 years ago
Find all complex numbers z satisfying...
iop360
 3 years ago
Find all complex numbers z satisfying...

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iop360
 3 years ago
Best ResponseYou've already chosen the best response.0\[z^3 = 27i\] Answers are: \[z = 3i\] \[z = \frac{ 3\sqrt{3} }{ 2 }  \frac{ 3i }{ 2 }\] \[z = \frac{ 3\sqrt{3} }{ 2 }  \frac{ 3i }{ 2 }\]

mayankdevnani
 3 years ago
Best ResponseYou've already chosen the best response.0http://au.answers.yahoo.com/question/index?qid=20100318052317AAjz850

mahmit2012
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1353827474036:dw

iop360
 3 years ago
Best ResponseYou've already chosen the best response.0i cant read the stuff at the top...

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2\[\huge i = e^{(3\pi/2 + 2n\pi)}\]\[\huge z^3 = 3^3e^{(3\pi/2 + 2n\pi)}\]

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2\[\huge z=\sqrt[3]{3^3}e^{(\large \frac{ 3\pi }{ 2 }+2n \pi)/3},\text{ } n=0,1,2\]

iop360
 3 years ago
Best ResponseYou've already chosen the best response.0how did you set up your first equation?

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2\[\huge z=3e^{\frac{ 3 \pi }{ 6 }+\frac{ 2 \pi }{ 3 }n},\text { }n=0,1,2\]

iop360
 3 years ago
Best ResponseYou've already chosen the best response.0can you please explain your steps

iop360
 3 years ago
Best ResponseYou've already chosen the best response.0for example, the 3pi/2 in the brackets

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2it's in the unit circle drawn above

iop360
 3 years ago
Best ResponseYou've already chosen the best response.0do you use eulers equation? z = r(cos(angle) + i sin(angle))

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2yes, just slightly different notation \[re^{x i}=r(\cos x + i \sin x)\] dw:1353828628571:dw

iop360
 3 years ago
Best ResponseYou've already chosen the best response.0only 1 question though, for your first equation i = ... if you have a negative i, does that always mean 3pi/2
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