complex question locus :( - help needed (1 Viewer)

[fuckit1991]

i was wondering how to solve fitzpatrick 31(f) q 6. |z^2-(zbar)^2|<4 . It reads absolue of z squared minus its conjugate squared is less than 4. Sketch and describe this region. Just an algebraic proof would be enuff tho. Thanks

 

[shady145]

the worked answers to the fitzpat book is on this site

 

[fuckit1991]

yeah i looked through it but for some reason the absolute value stays in the final answer..can someone explain this?

 

[lolokay]

let z=x+iy
you get |4ixy|<4
|xy|<1

which is just the area between the hyperbolas y=1/x, and y=-1/x

 

[tommykins]

 

[fuckit1991]

one thing why is there an absolute in the final value...
|4xyi|=sqrt(0+16x^2y^2)
=4xy...so y is there an absolute still in final answer?

. thanks for the help guys

 

[bv]

let z=x+iy
you get |4ixy|<4
|xy|<1

which is just the area between the hyperbolas y=1/x, and y=-1/x

ok i prob sound stupid.. but i think i missed something
where does the i go?

 

[tacogym27101990]

ok i prob sound stupid.. but i think i missed something
where does the i go?

|i|=1

 

[bv]

oh ok.. thanks