please help me understand this loci argand diagram question

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[dim anchor]

so it helps to draw it graphically. it's basically calculating the value of r such that it touches point (2,0), because as you know, no point exists there for arg(z-2) = 3pi/4, and because it's a ray pointing in one direction then you can imagine that increasing the radius beyond this point would only have one solution

ignore the part of the blue line below the y axis

so the second part is just them subbing in the point (2, 0)