Verified answer

Remember that |z - w| is the distance between z and w in the complex plane.

So |z - 3 + i| ≤ 5

<=> |z - (3 - i)| ≤ 5

i.e. z is within 5 units of the point 3-i.

So draw a circle of radius 5, centred at 3-i, and fill it in.

|z+i| ≤ |z-i|

says the distance from z to -i is less than or equal to the distance from z to +i.

In other words, take the perpendicular bisector of the line segment joining -i and +i; we want all points that are on this line or on the -i side of the line.

In this case the perpendicular bisector is just the real axis, so we just want everything on or below the real axis.