Question

complex number question

Answer 1

if complex number z satisfies mod(z-6i)=im(z)
then range of [arg(z)-arg(z bar)}=?

Answer 2

can u tell me what is the trajectory of mod(z-6i)=im(z)

Answer 3

i think it should be a parabola

Answer 4

wow correct its a parabola with focus 6i and directrix as real x axis
any prob? do u get it?

Answer 5

hmm yeah

Answer 6

now what is min and max value of arg z??

Answer 7

i dont know

Answer 8

well max(arg)=3*pi/4 and min(arg)=pi/4

Answer 9

ok now!!

Answer 10

\[\arg(z)-\arg(z ^{-})=2\arg(z)\]
ok!!

Answer 11

yeah so range=pi/2,3pi/2 ?????

Answer 12

yup :)

Answer 13

@experimentX take a look at this is it ok?

Answer 14

have to see ... will take a while.

Answer 15

let z = a+bi
|z-6i| = b => a^2 + (b-6)^2 = b^2 ... okay this is parabola.

Answer 16

yeah it is for sure

Answer 17

b = (a^2 + 36)/12