gerryliyana
COMPLEX VARIABLE



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gerryliyana
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electrokid
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what does that "*" represent?

gerryliyana
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* is equal to \(\times \)

electrokid
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a crossproduct?

gerryliyana
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no.., it just times

niksva
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@gerryliyana
solve for RHS first by using the values of dimensional vectors given in question

electrokid
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\[\vec{a}\times\vec{b}=\left\begin{matrix}
\hat{x}&\hat{y}&\hat{z}\\
u&v&0\\
x&y&0
\end{matrix}\right
=\hat{z}(uyvx)\\
\vec{a}\cdot\vec{b}=ux+vy\\
ab = (u+iv)(x+iy)=ux+i(vx)+i(uy)+(i^2)(xy)
\]

myko
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are you sure it's right? Because:
a.b=ux+vy
iz(axb)=i(uyxv)
and a*b=uxvy+i(uy+vx)
so it is not equal:
uxvy+i(uy+vx) =/= ux+vy+i(uyxv)

electrokid
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\[ab=(uyvx)+i(vx+uy)\]

gerryliyana
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its same with my answer @myko

gerryliyana
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yeah i think so

electrokid
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\[ab=\hat{z}\cdot(\vec{a}\times\vec{b})+i(\vec{a}\cdot\vec{b})\]

myko
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vx+uy =/= a.b
@electrokid

gerryliyana
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so what the right answer??

electrokid
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oh yea.. my bad..

electrokid
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that "*" in the question must be a complex conjugate

electrokid
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then it seems you might have it right.

gerryliyana
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good idea!! oh my bad...,

gerryliyana
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yeah,"*" means conjugate

electrokid
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always make sure that people are talking the same math language

gerryliyana
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thank you @electrokid

niksva
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@electrokid if "*" is complex conjugate then it will be rightly solved

gerryliyana
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i got it now.., thank you guys :)
