:| stupid complex question.... (1 Viewer)

[grimie]

can you have a look at this for me?

Sketch the region on the argand diagram that satisfies the inequality:
_ _
zz + 2(z+z) (lesser than or equal to) 0

do u understand that the second and fourth "z s" are conjuagtes? sorry - it is really hard to type maths quesitons on a normal comp

 

[Estel]

zz_+2(z+z_)<=0
x^2+y^2+4x<=0
(x+2)^2+y^2<=4

 

[grimie]

sorry......

when i tpyed, it the _ were above the correct z's. they are supposed to be above the second and the fourth.

 

[Estel]

z_ denotes z bar in my answer.

 

[grimie]

yeah.... no help. that is the process that they use in the answers, but i cannot see how it works...

zz_ = |z| ^2?

|z|^2 = x^2 + y^2?

i am just completely confused with this quesiton.....

 

[Estel]

what you have written is correct.

zz_=(x+iy)(x-iy)=x^2+y^2=|z|^2

 

[Shuter]

can you have a look at this for me?

Sketch the region on the argand diagram that satisfies the inequality:
_ _
zz + 2(z+z) (lesser than or equal to) 0

do u understand that the second and fourth "z s" are conjuagtes? sorry - it is really hard to type maths quesitons on a normal comp

_
z=x-iy
z=x+iy
_
zz= x^2 + y^2

2(z+congZ)= 2(x+iy) + 2(x-iy) = 4x

_
zz + 2(congZ) = x^2 + y^2 + 4x <= 0

you should be able to graph and shade that.

Wait I'll try

(x+2)^2 + y^2 - 4 <=0
(x+2)^2 + y^2 <=4

therefore circle radius 2, center (-2, 0)

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[gordo]

just sub in z=x+iy and then expand it all and complete the square

 

[Shuter]

Did I do it right? Maybe I know more 4U than I thought.