# arg(z+2+2i)=2pi/3 - is my book wrong?

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My book tells me to sketch the locus of arg(z+2+2i)=2pi/3 but if you simplify you get arg(x+2) + (y+2)i)=2pi/3 when you x=1 y=1 you get pi/4. In fact you can do this for any value foe when x=y and you get pi/4. If not what values of x and y do you get?

In the answer it says x<-2 and y>-2 so if you use x=-3 and y=-1 you get 3/4 pi

In the answer it says x<-2 and y>-2 so if you use x=-3 and y=-1 you get 3/4 pi

Last edited by Mad Man; 4 weeks ago

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(Original post by

Would you know how to sketch the locus: arg(z) = 2pi/3?

**DFranklin**)Would you know how to sketch the locus: arg(z) = 2pi/3?

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#7

(Original post by

yes It is a line that goes from the origin at counterclockwise angle of 2pi/3 but it starts at the origin.

**Mad Man**)yes It is a line that goes from the origin at counterclockwise angle of 2pi/3 but it starts at the origin.

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(Original post by

Well, if arg(u) = 2pi/3, and z = u - 2 - 2i, can you see how this means that arg(z+2+2i) = 2pi/3?

**DFranklin**)Well, if arg(u) = 2pi/3, and z = u - 2 - 2i, can you see how this means that arg(z+2+2i) = 2pi/3?

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Oh wait, the numbers cancel out right? But is there a graph calculator that uses argand diagrams I want to visualise it please

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(Original post by

In the answer it says x<-2 and y>-2 so if you use x=-3 and y=-1 you get 3/4 pi

**Mad Man**)In the answer it says x<-2 and y>-2 so if you use x=-3 and y=-1 you get 3/4 pi

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#12

(Original post by

no can you please explain?

**Mad Man**)no can you please explain?

So this means that if you know the locus of u (which you described in post #3), and you shift that by -2 - 2i, you will get the locus for z.

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#13

(Original post by

Why is this the case though. What I am saying is that is there a value of x and y for z=x+iy to get arg(z+2+2i)=2pi/3?

**Mad Man**)Why is this the case though. What I am saying is that is there a value of x and y for z=x+iy to get arg(z+2+2i)=2pi/3?

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(Original post by

Yes. Again, would you know how to find values for x and y so that if u = x+iy then arg(u) = pi/3?

**DFranklin**)Yes. Again, would you know how to find values for x and y so that if u = x+iy then arg(u) = pi/3?

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**DFranklin**)

Yes. Again, would you know how to find values for x and y so that if u = x+iy then arg(u) = pi/3?

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#16

(Original post by

Would you sub in values for x and y and use the arg button on your calculator?

**Mad Man**)Would you sub in values for x and y and use the arg button on your calculator?

So, here's a

**basic fact you should know.**The point z with |z| = R (i.e. distance from the origin = R) and argument theta is .

Edit: however, you don't need this to sketch the locus. You know the angle the line has to go in (post #3), and you know where it starts from (post #12). So you don't need equations for x and y.

Last edited by DFranklin; 4 weeks ago

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**DFranklin**)

Yes. Again, would you know how to find values for x and y so that if u = x+iy then arg(u) = pi/3?

(Original post by

That's going to tell you what arg(x+iy) is, but it's not going to tell you how to find x and y to give a particular argument.

So, here's a

**DFranklin**)That's going to tell you what arg(x+iy) is, but it's not going to tell you how to find x and y to give a particular argument.

So, here's a

**basic fact you should know.**The point z with |z| = R (i.e. distance from the origin = R) and argument theta is .
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#18

(Original post by

Oh yeah I knew that, it was on the last page on my book, I'll try and work what x and y are then.

**Mad Man**)Oh yeah I knew that, it was on the last page on my book, I'll try and work what x and y are then.

**You don't need to know what x and y are.**(See edit to previous post).

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(Original post by

That's going to tell you what arg(x+iy) is, but it's not going to tell you how to find x and y to give a particular argument.

So, here's a

Edit: however, you don't need this to sketch the locus. You know the angle the line has to go in (post #3), and you know where it starts from (post #12). So you don't need equations for x and y.

**DFranklin**)That's going to tell you what arg(x+iy) is, but it's not going to tell you how to find x and y to give a particular argument.

So, here's a

**basic fact you should know.**The point z with |z| = R (i.e. distance from the origin = R) and argument theta is .Edit: however, you don't need this to sketch the locus. You know the angle the line has to go in (post #3), and you know where it starts from (post #12). So you don't need equations for x and y.

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(Original post by

Please wait I need to show you what my book says and I want to see if you agree with it because it says you need to form an equation for x and y

**Mad Man**)Please wait I need to show you what my book says and I want to see if you agree with it because it says you need to form an equation for x and y

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