Final answer:
The Cartesian equation for the given locus Arg(z-2-i)=π/4 is the line (y-1) = (x-2). It has a slope of 1 and passes through the point (2,1) in the Cartesian coordinate system.
Step-by-step explanation:
To find the Cartesian equation represented by the locus Arg(z-2-i)=π/4, we first need to understand that z can be represented as x + yi, where x and y are the real and imaginary components, respectively. Thus, z-2-i becomes (x-2) + (y-1)i. The argument of a complex number is the angle it makes with the positive real axis in the complex plane, and in this case, the angle given is π/4 radians or 45 degrees.
The equation Arg((x-2) + (y-1)i) = π/4 implies the ratio of the imaginary part to the real part (y-1)/(x-2) is tantamount to the tangent of 45 degrees, which is 1. Hence, (y-1) = (x-2). This is a straight line with a slope of 1 through the point (2,1) in the Cartesian coordinate system.