area of region (1 Viewer)

[juantheron]

Area of Region bounded by the locus of that satisfying

 

[Nooblet94]

Area of Region bounded by the locus of that satisfying

EDIT: Disregard that, I was entirely wrong - changing my answer to 25(2+3pi). I don't have time to write out my working, but hopefully someone can check that.

 

[kingkong123]

i got ??? if the argument is then it will be of a circle, but because its there will be 2 three quarter circles of radius 5. so i just did

 

[math man]

EDIT: in this case angle between two vectors isnt pi/4 i worked it out to be 3pi/4 which changes the answer

 

[bleakarcher]

Im confused with this question on where the pi/4 goes and why. Can someone help?

 

[bleakarcher]

how can you just assume that? can you prove it? its pretty clear when the chords are drawn from a point on the x-axis using the fact that the exterior angle to a triangle is equal to the sum of the interior angles (whereas the points lie on the y-axis).

 

[bleakarcher]

can someone explain?

 

[math man]

The proof for 3pi/4 is:

 

[bleakarcher]

^ in that case the angle is not always the one formed between the two vectors yeh? you have to work it out geometrically right?

 

[math man]

^ in that case the angle is not always the one formed between the two vectors yeh? you have to work it out geometrically right?

i would have to say if it is bounded by axis then yes

 

[Nooblet94]

View attachment 24376

EDIT: in this case angle between two vectors isnt pi/4 i worked it out to be 3pi/4 which changes the answer

Wow, I cannot believe I got that right. My method was completely different though - a lot longer and harder and altogether less efficient.

 

[bleakarcher]

Mathman, I understood how you worked out 3pi/4 but Im struggling to do myself when working on the left hand side of the plane. Help me out? Is there a simpler way to determining the included angle?

 

[bleakarcher]

Also, I placed the point P representing z on the x-axis.

 

[math man]

on the LHS of the plane arg(z+5i)-arg(z-5i) = pi/4, try that if you havent already

 

[bleakarcher]

yeh i knew that but I still need help lol.

 

[bleakarcher]

The geometry in finding the included angle is what is confusing me.

 

[math man]

 

[bleakarcher]

You marked the angle theta incorrectly there so I'm kinda confused since it represents the argument of the vector representing z-5.

 

[bleakarcher]

yeh its not its argument?

 

[math man]

yes the angle you marked is theta, but theta represents a pos value and clearly the arg is neg