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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.
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.
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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