Complex numbers problem

kelxx

Sketch Argand Diagrams to represant the complex z = x+yi which satisfy the following conditions:

|2z| = |z| + 6

Thanks!

TheBody

kelxx wrote: »

Sketch Argand Diagrams to represant the complex z = x+yi which satisfy the following conditions:

|2z| = |z| + 6

Thanks!

Well we can't give you the solution as it's against the charter so have you got any ideas? You are being asked to sketch on an argand diagram all the numbers that satisfy the equation. Might be helpful to do the following to get you started:

We can rewrite |2z|=|z|+6 as 2|z|=|z|+6. Any idea what we could do next?

kelxx

that is the part im actually stuck with... i dont see how |2z| is the same as 2|z|

|2z| = √ ((2x)^2 + (2y)^2)

2|z| = 2√(x^2 + y^2)

?

TheBody

kelxx wrote: »

that is the part im actually stuck with... i dont see how |2z| is the same as 2|z|

|2z| = √ ((2x)^2 + (2y)^2)

2|z| = 2√(x^2 + y^2)

?

Ah ok. I'll show you why that is true.

[Latex]|2z|=| 2(x+yi)|[/Latex]
[Latex]=|2x+2yi|[/Latex]
[Latex]=\sqrt{(2x)^2+(2y)^2}[/Latex]
[Latex]=\sqrt{4x^2+4y^2}[/Latex]
[Latex]=\sqrt{4(x^2+y^2)}[/Latex]
[Latex]=2\sqrt{x^2+y^2}[/Latex]
[Latex]=2|z|[/Latex]

Does that make sense?

kelxx

Ah yes i understand now! Thanks for the help!!

TheBody

No problem. Glad I could help!!