What is the locus of `z ,`if amplitude of `(z-2-3i)`is `pi/4?`

1.	What is the locus of `z ,`if amplitude of `(z-2-3i)`is `pi/4?`
Answer» As `z = x+iy` `:. z-2-3i = x+iy-2-3i =(x-2)+i(y-3)` As `pi/4` is the amplitude of ` (x-2)+i(y-3)`, `:. tan (pi/4) = (y-3)/(x-2)` `=>1 = (y-3)/(x-2)` `=>y-3 = x-2` `=> x - y +1 = 0`, which is the locus of `z`. `:.` Locus of `z` represents a straight line.

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What is the locus of `z ,`if amplitude of `(z-2-3i)`is `pi/4?`

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