Question

COMPLEX VARIABLE

Answer 1

what does that "*" represent?

Answer 2

* is equal to \(\times \)

Answer 3

a cross-product?

Answer 4

no.., it just times

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

\[ab=(uy-vx)+i(vx+uy)\]

Answer 9

its same with my answer @myko

Answer 10

yeah i think so

Answer 11

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

Answer 12

vx+uy =/= a.b
@electrokid

Answer 13

so what the right answer??

Answer 14

oh yea.. my bad..

Answer 15

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

Answer 16

then it seems you might have it right.

Answer 17

good idea!! oh my bad...,

Answer 18

yeah,"*" means conjugate

Answer 19

always make sure that people are talking the same math language

Answer 20

thank you @electrokid

Answer 21

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

Answer 22

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

Answer 23

by the way.., if all of you have a facebook., add me on facebook
http://www.facebook.com/gerry.resmiliyana
thank you so much!