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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We are given 2 + iz = i. Now we find z using the relation given

2 + iz = i

=>  z = (i - 2)/i

=> z = 1 - 2/i = 1 - 2i/i^2 = 1 + 2i

The absolute value is |z| is given by sqrt ( 1^2 + 2^2)

= sqrt ( 5)

The required absolute value of z is sqrt 5.

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

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

We find the value of z first from the given equation:

2+iz = i.

=> 2+iz-2 = i - 2.

=> iz = i-2.

=> iz/i = (i-2)/i

=> z = i/i - 2/i

=> z = 1-2*t//i*i

=> z = 1- 2i/(-1), as i^2 = -1.

=> z = 1+2i.................(1).

To find the absolute value of z.

We know absolute value of x+yi = |x+yi| = sqrt(x^2+y^2).

Therefore the absolute vale of z = 1+2i is given by :

|z| = |1+2i| = sqrt(1^2+2^2) = sqrt5.

Therefore  z = 1+2i.

Absolute of valie of z = |z| = sqrt5.

Top Answer

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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