Determine the absolute value Determine the absolute value of

Determine the absolute value.

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

Solution

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.