Absolute value of zFind the absolute value of z if i(z-1) = -2
We need the absolute value of x given that i(z-1) = -2
i(z-1) = -2
=> z - 1 = -2/i
=> z = -2/i + 1
=> z = -2*i/i^2 + 1
=> z = -2i / -1 + 1
=> z = 1 + 2i
The absolute value of z is sqrt (1^2 + 2^2) = sqrt (1 + 4) = sqrt 5.
To determine the absolute value of the complex number, we'll write it in the rectangular form.
For this reason, we'll re-write z, isolating z to the left side. For this reason, we'll remove the brackets:
iz - i = - 2
We'll add i both sides:
iz = i - 2
We'll divide by i both sides:
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
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