Question

Complex number problem....

Answer 1

Click the attachment

Answer 2

Any idea how to solve?

Answer 3

HI!!

Answer 4

i have an idea, not sure if it will work or not

Answer 5

since it doesn't matter what the numbers are, maybe we can make an example and see what happens
also i changed the last requirement to \(|z_1|=|z_2|=|z_3|+1\) to make life easier figuring we can adjust at the end

Answer 6

then the three numbers i picked that fit both those requirements are
\[\frac{1}{2}+\frac{\sqrt3}{2}i,\frac{1}{2}-\frac{\sqrt3}{2}i,-1\]

Answer 7

probably a much more elegant way to do it, but i don't know one
maybe @Zarkon has a better idea

Answer 8

that is what I did to get the final answer (it is a cheat) ;)

Answer 9

you assume |z1|=|z2|=|z3|=1 instead of |z1|=|z2|=|z3| = 1/sqrt3 @misty1212

Answer 10

btw i made a typo, meant \[|z_1|=|z_2|=|z_3|=1\]

Answer 11

though I didn't use -1

Answer 12

what did you use?

Answer 13

oh let me guess, same ones i used except you used \(-\frac{1}{2}\) and \(1\) for the real parts

Answer 14

what is the "not cheat" method?

Answer 15

\[\frac{-1}{\sqrt{3}}\]

and
\[\frac{1}{2\sqrt{3}}\pm\frac{1}{2}i\]

Answer 16

Will these values satify z1,z2,z3 @Zarkon

Answer 17

oops corrected nvm

Answer 18

yes these values will work and give you the answer

Answer 19

to do it in general you would probably want to use polar notation

Answer 20

BUt modulus of \[-1/\sqrt{3}\] will not give 1/sqrt3

Answer 21

try it again

Answer 22

and don't think too hard either

Answer 23

\[-1/\sqrt{3}\] is a real number

Answer 24

And whats its modulus

Answer 25

means the absolute value

Answer 26

for a real number it is just that

Answer 27

@Zarkon cannot reply

Answer 28

\[\frac{1}{2\sqrt{3}}\pm\frac{1}{2}i\] modulus of this

Answer 29

Can u help in this
?