Find equation of loci for:

Question

arg(z+3)=pi/4?

Answer 1

arz(z + 3) = π/4.

arz(x + iy + 3) = π/4.

arz[(x + 3) + iy] = π/4.

We know that θ = arg z = tan^-1(y/x).

tan^-1[y/(x + 3)] = π/4.

y/(x + 3) = tan(π/4)

y/(x + 3) = 1

y = x + 3

The locus is y = x + 3.