Grrr locus question xD (1 Viewer)

[NubMuncher]

|w| = 10 and arg w is between and including 0 and pi/2.
z= 3 + 4i + w.

What is the locus of z?

I know the locus of w is a circle at origin with radius 10 and only values in the first quadrant are accepted, however I'm not sure on how to find the locus of a complex number involving another variable complex number.

Any help appreciated : )

 

[ohexploitable]

Just a guess but...

You should be able to see that it's the original circle shifted by 4 units upwards and 3 units to the right.

 

[NubMuncher]

I have no idea what the correct answer is. My gay ass textbook doesn't have an answer for this question : (

 

[Bored Of Fail 3]

Just a guess but...

think the second bracket should be (y-4)^2

and you need to state restrictions

 

[Bored Of Fail 3]

you originally started with x^2 +y^2 =10^2

but you shift all the real parts to the right 3, and shift imaginary parts up 4

so (x-3)^2 +(y-4)^2 =100 and then state restrictions

 

[ohexploitable]

think the second bracket should be (y-4)^2

and you need to state restrictions

Fixed.

 

[ohexploitable]

See updated post.

 

[NubMuncher]

So those restrictions are due to the argument restrictions on w right?

 

[Bored Of Fail 3]

So those restrictions are due to the argument restrictions on w right?

yes

 

[Riproot]

Paint?

 

[ohexploitable]

Paint?

^_^

 

[Riproot]

^_^

Well done, it looks better than the diagrams in my books.

 

[deterministic]

Just a guess but...




You should be able to see that it's the original circle shifted by 4 units upwards and 3 units to the right.

Correct. Algebraically, do this:
|w|=10 and 0<=arg(w)<=pi/2
z=3+4i+w so w=z-3-4i
So |z-3-4i|=|w|=10 with restrictions that 0<=arg(z-3-4i)<=pi/2, which is clearly the answer.