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What is the locus of z , if amplitude o...

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

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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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