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

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starshippiy | Student, College Freshman | eNoter

Posted May 5, 2011 at 4:00 AM via web

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z=?

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

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giorgiana1976 | College Teacher | Valedictorian

Posted May 5, 2011 at 5:56 AM (Answer #2)

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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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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 7, 2011 at 10:30 AM (Answer #3)

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It is given that 3z -9i = 8i + z + 4

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

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

=> 2z = 4 + 17i

=> z = 2 + 17i/2

|z| = sqrt (2^2 + (17/2)^2)

=> sqrt (4 + 289/4)

=> sqrt (305/4)

=> (sqrt 305)/2

The value of |z| = (sqrt 305)/2

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