Hey guys, quick question

(b) Find all complex solutions of iz + z = 0 and sketch them in the complex plane.

Well I let z = x + iy, simplified and obtained x - y + i(x - y) = 0

But as for sketching them I'm not entirely sure how to proceed. The answers have up and until the answer I obtained but then immediately proceeds to sketching y = x

Can someone please explain why y = x is the solution?