Determine the absolute value of z if z-1 = -2/i .

To find 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.

z = 1 -
2/i

We'll multiply by i:

z = (i -
2)/i

Since we have to put z in the rectangular form and since we are
not allowed to keep a complex number to the denominator, 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

We'll write the
rectangulat form of z:

z = x + y*i

The
real part is: Re(z) = x.

The imaginary part is: Im(z) =
y

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

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

|z| = sqrt(1 + 4)

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