What is the absolute value of z if 3z -9i = 8i + z + 4.

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The module of z represents the distance:

|z| = sqrt(Re(z)^2 + Im(z)^2)

We must determine the rectangular form of z, from the given expression:

3z -9i = 8i + z + 4

We'll isolate z to the left side. For this reason, we'll subtract z both sides:

2z - 9i = 8i + 4

We'll add 9i both sides:

2z = 4 + 17i

We'll divide by 2:

z = 2 + 17i/2

Comparing, we'll get:

Re(z) = 2

Im(z) = 17/2

|z| = sqrt(4 + 289/4)

|z| = sqrt305/2

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