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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The absolute value of z has to be found if 2+iz=i

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

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