Jonothancroller
Member
- Joined
- Sep 9, 2015
- Messages
- 53
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- Male
- HSC
- 2016
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
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But .... it's a locus question .... you haven't explained that the first one is a circular arc.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.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
Oh right because anticlockwise is in the positive directionFor the image you provided, the point should be BELOW the x-axis.