Rivalry's Complex Numbers Troubles (1 Viewer)

[RivalryofTroll]

Sketch the region on the Argand Diagram (z* is z conjugate)

|z^2 - z*^2 | ≤ 1

My working out
|4xyi| ≤ 1
I got y ≤ 1/4x, am I wrong?

I'll post more questions later when I need help.

 

[deswa1]

Yep thats right (assuming you meant 1/(4x) -> like have the x on the denominator)

 

[RivalryofTroll]

(1/z) + (1/z*) ≤ 1

does this become:

(x-1)^2 + y^2 >= 1?

Double-checking.

 

[barbernator]

yep

 

[SpiralFlex]

(1/z) + (1/z*) ≤ 1

does this become:

(x-1)^2 + y^2 >= 1?

Double-checking.

Rote learner alert. You are missing an important concept. Clue: fraction. Though your working is right, I feel as though I need to point this out.

 

[RivalryofTroll]

Rote learner alert. You are missing an important concept. Clue: fraction. Though your working is right, I feel as though I need to point this out.

idgi?

I just used mindless algebra from z = x+iy and yeah.

Explain pls.

 

[barbernator]

idgi?

I just used mindless algebra from z = x+iy and yeah.

Explain pls.

1/0 is undefined, so you need to restrict the function.

 

[braintic]

Yep thats right (assuming you meant 1/(4x) -> like have the x on the denominator)

Actually, it's NOT correct.

In the second last line, the i can be dropped, giving |xy|≤1/4.
To remove the absolute values, you must handle the 4 cases where x and y are alternately positive and negative.
The graph of this relation is the region 'bounded' by the TWO curves xy=1/4 and xy=-1/4.

 

[SpiralFlex]

Let's say if the question was












Algebra is all good, however - can (0,0) be a point?

Think about fractions. If the question had an equals to, you would draw a hole at (0,0). This is where many get trapped. Mindless algebra may not always do the trick.

 

[deswa1]

Actually, it's NOT correct.

In the second last line, the i can be dropped, giving |xy|≤1/4.
To remove the absolute values, you must handle the 4 cases where x and y are alternately positive and negative.
The graph of this relation is the region 'bounded' by the TWO curves xy=1/4 and xy=-1/4.

Yep true. This is right

 

[RivalryofTroll]

Let's say if the question was












Algebra is all good, however - can (0,0) be a point?

Think about fractions. If the question had an equals to, you would draw a hole at (0,0). This is where many get trapped. Mindless algebra may not always do the trick.

oh thanks Spiral.

Actually, it's NOT correct.

In the second last line, the i can be dropped, giving |xy|≤1/4.
To remove the absolute values, you must handle the 4 cases where x and y are alternately positive and negative.
The graph of this relation is the region 'bounded' by the TWO curves xy=1/4 and xy=-1/4.

yeah i realised afterwards but thanks.

 

[OMGITzJustin]

Let's say if the question was












Algebra is all good, however - can (0,0) be a point?

Think about fractions. If the question had an equals to, you would draw a hole at (0,0). This is where many get trapped. Mindless algebra may not always do the trick.

first time where I've seen spiral get angry

 

[hamster-lol]

omg you guys are so smart

I've started complex numbers these holidays, but I've got no idea about some of the stuff in this thread.

 

[asianese]

^ pls enjoy yr11. Drop everything.

 

[hamster-lol]

^ pls enjoy yr11. Drop everything.

But year 11 is over, year 12 starts in just over a week from now!

 

[SpiralFlex]

Just want to point out that when doing loci questions always look out for ANY restrictions. This is the case with complex numbers and with conic sections.