drawing Arg(z) graph ? open circle at origin?

[joechan521]

when drawing a ray, something like arg(z)= pi/4
does the origin has to be drawn with an open circle???
since its not defined

[Ahmad]

Since arg(0) is undefined, it should be an open circle.

[joechan521]

oh, my damn text book doesn't take that into account

[Ahmad]

It may be right. Check what VCAA does to make sure.

[joechan521]

how to check that? in study design? would they have such a minor thing?

[enwiabe]

Check by logic!

z = x+yi

Arg(z) = tan^-1(y/x)

if x = 0 and y = 0 then you get tan^-1(0/0) which is clearly undefined.

Also, this was an issue on one of the exams from 2000-2002 that was covered in the assessment report. Not entirely sure which though.

[joechan521]

my text book must be shit then
and it say its a new edition this yr, but theres more wrong answers than correct ones

[Khangfu]

You should not test it like that. Just note that y/x, means x>0  or else Arg(z) is undefined.

[enwiabe]

That's... more or less the same thing?

[brendan]

It may be right. Check what VCAA does to make sure.

you don't need to. Arg(0+0i) is undefined

[Khangfu]

in my view the difference is i accounted for everything and you used only (0,0) as an example. Which is all fine for this case butfor other things it might not work ... like proving for instance.

[Collin Li]

Commonsense dictates Arg(0) is undefined. What is the angle within the principal argument for 0+0i from a centre 0+0i?

Uhm, could be pi, could be 3pi/4, could be e... pick your favourite number in between (-pi, pi].

Therefore, it's not defined.

[boulos90]

Check by logic!

z = x+yi

Arg(z) = tan^-1(y/x)

if x = 0 and y = 0 then you get tan^-1(0/0) which is clearly undefined.

Also, this was an issue on one of the exams from 2000-2002 that was covered in the assessment report. Not entirely sure which though.

Chuck norris can divide by zero

[joechan521]

we all know its undefined, i was asking whether we need to draw an open circle when graphing it.

probably should draw it to be safe

[Collin Li]

we all know its undefined, i was asking whether we need to draw an open circle when graphing it.

probably should draw it to be safe

You must draw an open circle when graphing it. It will be checked.