Rays

[lisafaustina]

Ok so when u have somethig like
Sketch {z: Arg(z) < -pi/4 } how do you sketch this in the complex plane? I dunno which area to shade in..

[ghadz7]

The angle from (0,0) is lower than -pi/4.

[lisafaustina]

Could someone please roughly sketch this graph?

[jto1292]

Shade all of quadrant 3 and the half of quad 4 that's UNDER the *ray*. Have the *ray* dotted.. I think that's right. Correct me if wrong anyone..

Lol soz kept referring to the ray as arc**

[98.40_for_sure]

Don't forget to open circle the origin and dotted lines!

[jto1292]

Negative Re(z) axis should also be dotted.. and yes, open circle on origin

[JinXi]

1 thing i feel weird about, is when they give u an axis and ask u to sketch like Arg(z)=-pi/4, how are we supposed to dot the -ve x axis so that its clear-.-

[98.40_for_sure]

Lol it's hard to draw a frickin dotted line OVER their lines usually i use a red pen to do it but scared i can't rub it out if it turns out to be incorrect

[jto1292]

agreed. I always get scared I'm doing it wrong.. Thanks for this question though, coz I remembered I need to revise region shading in complex plane....

[lisafaustina]

Thanks. What if it's like {z: Arg(z) < or = -pi/4}
and what if it's  {z: Arg(z) > -pi/4}

when do you have an open circle on origin and when do you have a closed circle?

[98.40_for_sure]

{z: Arg(z) < or = -pi/4} is dotted -ve Re(z) axis and full line at -pi/4

{z: Arg(z) > -pi/4} is dotted line at pi/4 and full line at -ve Re(z) axis as -pi<Arg(z)< and = pi

[jto1292]

Rays always have open circle on their starting point. If it's Arg(z), (0,0) has open circle. If it's Arg(z-(1+3i), (1,3) has an open circle. Arg(z) < or = to -pi/4 means make the ray solid, not dotted, but KEEP negative Re(z) axis dotted. EDIT: Also keep same shading as Arg(z) < -pi/4..

 Arg(z) > -pi/4 means dotted ray and shade quad 1 2 and the half of 4 that's above the ray, NO quad 4. Also dot the neg Re(z) axis.

[JinXi]

Rays always have open circle on their starting point. If it's Arg(z), (0,0) has open circle. If it's Arg(z-(1+3i), (1,3) has an open circle. Arg(z) < or = to -pi/4 means make the ray solid, not dotted, but KEEP negative Re(z) axis dotted. EDIT: Also keep same shading as Arg(z) < -pi/4..

 Arg(z) > -pi/4 means dotted ray and shade quad 1 2 and the half of 4 that's above the ray, NO quad 4. Also dot the neg Re(z) axis.

Arg(z) > something , doesn't that mean -ve x axis is solid, since -pi < Arg(z) </= pi.

[jto1292]

Rays always have open circle on their starting point. If it's Arg(z), (0,0) has open circle. If it's Arg(z-(1+3i), (1,3) has an open circle. Arg(z) < or = to -pi/4 means make the ray solid, not dotted, but KEEP negative Re(z) axis dotted. EDIT: Also keep same shading as Arg(z) < -pi/4..

 Arg(z) > -pi/4 means dotted ray and shade quad 1 2 and the half of 4 that's above the ray, NO quad 4. Also dot the neg Re(z) axis.

Arg(z) > something , doesn't that mean -ve x axis is solid, since -pi (greater) Arg(z) (greater of equal to) pi.

Good point. You're probs right... Neg Re(z) axis being dotted should only happen on instances such as Arg(z) > pi/4. Good pick up. Sorry about confusion :S

[jto1292]

OKEY so for further clarification, Arg(z) > and = or > angle means DOT -ve Re(z). Arg(z)< or = or < angle means -ve Re(z) should be included...