Question

Arg(Z)<=pi/3 where Z is complex and -pi 13 years ago

Answer 1

?

Answer 2

graphj?

Answer 3

How can ArgZ be less than pi and pi/3 at the same time?

Answer 4

sorry i meant the principle value of Arg(Z) is defined to be between (-pi,pi] so it ends up as -pi<Arg(Z)<=pi/3

Answer 5

Yup, sin < sqrt3/2 and cos < 1/2

Answer 6

thanks guy.. can you show working?? how to get to answer

Answer 7

There is not much working involved. The arg of a complex number is basicly an angle that this number has with positive real axis when represented geometricly. So puting this angle between to bounds (-pi,pi/3) gives a sector of the plane.

Answer 8

hm what about if i wanna do \[Arg(Z)=\frac{\pi}{3}\] .. let Z=x+yi .: y/x=tan(pi/3) \[y=\sqrt{3}x \] but how do i get the restriction x>0?

Answer 9

Arg(z)=pi/3 is just a ray from the origin

Answer 10

@estudier how did you do that??

Answer 11

what if its Arg(Z+3)?

Answer 12

it could be anything. Think of it this way: 3 is also a complex number, just like Z. So their sum is:

Answer 13

i meant Arg(Z+3)=pi/3

Answer 14

It's just the sin and cos values for pi/3....

Answer 15

how u get sin< and cos<?

Answer 16

|z|(cos arg z+i sin arg z)

Answer 17

what is that??

Answer 18

geometric representation of a complex number

Answer 19

explain?