Absolute value of zFind the absolute value of z if i(z-1) = -2

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We need the absolute value of x given that i(z-1) = -2

i(z-1) = -2

=> z - 1 = -2/i

=> z = -2/i + 1

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

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

=> z = 1 + 2i

The absolute value of z is sqrt (1^2 + 2^2) = sqrt (1 + 4) = sqrt 5.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine the absolute value of the complex number, we'll write it in the rectangular form.

For this reason, we'll re-write z, isolating z to the left side. For this reason, we'll remove the brackets:

iz - i = - 2

We'll add i both sides:

iz = i - 2

We'll divide by i both sides:

z = (i - 2)/i

Since we have to put z in the rectangular form and since we are not allowed to keep a complex number to the denominator, 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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