OpenStudy (hysenberg):

complex number question

3 years ago
OpenStudy (hysenberg):

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

3 years ago
OpenStudy (sidsiddhartha):

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

3 years ago
OpenStudy (hysenberg):

i think it should be a parabola

3 years ago
OpenStudy (sidsiddhartha):

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

3 years ago
OpenStudy (hysenberg):

hmm yeah

3 years ago
OpenStudy (sidsiddhartha):

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

3 years ago
OpenStudy (hysenberg):

i dont know

3 years ago
OpenStudy (sidsiddhartha):

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

3 years ago
OpenStudy (hysenberg):

ok now!!

3 years ago
OpenStudy (sidsiddhartha):

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

3 years ago
OpenStudy (hysenberg):

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

3 years ago
OpenStudy (sidsiddhartha):

yup :)

3 years ago
OpenStudy (hysenberg):

@experimentX take a look at this is it ok?

3 years ago
OpenStudy (experimentx):

have to see ... will take a while.

3 years ago
OpenStudy (experimentx):

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

3 years ago
OpenStudy (hysenberg):

yeah it is for sure

3 years ago
OpenStudy (experimentx):

b = (a^2 + 36)/12|dw:1400357918499:dw|

3 years ago