How to find the locus of Arg((z-z1)/(z-z2)) = β

Find the locus of Arg((z-z1)/(z-z2)) = β

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[mxpph]

Finally someone who can explain it fully, however how can you know where the centre of the circle is?

[harshjariwala]

it would be much appreciated if you can provide more examples using beta = pi/3 or pi/6 or pi/2

[prasadjoshi]

Could u please state the coordinates of the centre of the arc. Thanks

[adelekeademolu]

Much thanks. That means if beta is 0°, z must be a straight line between z1 and z2, on the assumption that z1≠z2. Am I right?