Determine the absolute value.Determine the absolute value of z for 2+iz=i
The absolute value of z has to be found if 2+iz=i
=> i*z = i - 2
=> i^2*z = i^2 - 2i
=> -z = -1 - 2i
=> z = 1 + 2i
|z| = sqrt (1^2 + 2^2)
=> sqrt(4 + 1)
=> sqrt 5
The absolute value of z is sqrt 5
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.