Determine the absolute value of z for 2+iz=i

To determine the absolute value of the complex number,
we'll put it in the rectangular form first.

For this
reason, we'll re-write z, isolating z to the left side. For this reason, we'll subtract
2 both sides:

iz = i - 2

We'll
divide by i:

z = (i -
2)/i

Since we have to put z in the rectangular
form:

z = x + i*y, we'll multiply the ratio by the
conjugate of i, that is -i.

z = -i*(i -
2)/-i^2

But i^2 = -1

z = -i*(i
- 2)/-(-1)

We'll remove the
brackets:

z = 2i - i^2

z = 1 +
2i

The modulus of z: |z| = sqrt (x^2 +
y^2)

We'll identify x = 1 and y =
2.

|z| = sqrt(1 +
4)

The absolute value of the complex number z
is: |z|  = sqrt 5.