Complex number locus questions (1 Viewer)

[Jonothancroller]

Hey, can someone explain the locus questions such as arg(z-a)-arg(z-b)=θ, because I don't really understand them. Same with arg(z-a)+arg(z-b)=θ

 

[kawaiipotato]

arg(z-a)-arg(z-b)=θ,











http://imgur.com/DdFDE9p (I assumed b>a)

This is the same for arg(z-a) + arg(z-b) = theta
by taking out the negative for arg(z-b) giving
arg(z-a) - (-arg(z-b)) = theta
arg(z-a) - arg(1/(z-b)) = theta
And then drawing vectors z-a and 1/(z-b), labelling the angle between them as theta, starting from 1/(z-b) to z-a

 

[braintic]

arg(z-a)-arg(z-b)=θ,











http://imgur.com/DdFDE9p (I assumed b>a)

This is the same for arg(z-a) + arg(z-b) = theta
by taking out the negative for arg(z-b) giving
arg(z-a) - (-arg(z-b)) = theta
arg(z-a) - arg(1/(z-b)) = theta
And then drawing vectors z-a and 1/(z-b), labelling the angle between them as theta, starting from 1/(z-b) to z-a

But .... it's a locus question .... you haven't explained that the first one is a circular arc.
And what are you claiming is the shape of the second example?

 

[RealiseNothing]

arg(z-a)-arg(z-b)=θ,











http://imgur.com/DdFDE9p (I assumed b>a)

This is the same for arg(z-a) + arg(z-b) = theta
by taking out the negative for arg(z-b) giving
arg(z-a) - (-arg(z-b)) = theta
arg(z-a) - arg(1/(z-b)) = theta
And then drawing vectors z-a and 1/(z-b), labelling the angle between them as theta, starting from 1/(z-b) to z-a

For the image you provided, the point should be BELOW the x-axis.

 

[kawaiipotato]

For the image you provided, the point should be BELOW the x-axis.

Oh right because anticlockwise is in the positive direction