Determine the absolute value of z if z-1 = -2/i .

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

z-1 = -2/i

=> z = 1-2/i

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

=> z = 1-2i/-1

=> z = 1+2i

=> absolute z =|z| = |1+2i|

=> |z| = sqrt(1+2^2)

=>|z| = sqrt5.

Top Answer

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To find 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.

z = 1 - 2/i

We'll multiply by i:

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

We'll write the rectangulat form of z:

z = x + y*i

The real part is: Re(z) = x.

The imaginary part is: Im(z) = y

The modulus of z: |z| = sqrt (x^2 + y^2)

We'll identify x = 1 and y = 2.

|z| = sqrt(1 + 4)

The requested absolute value of the complex number z is: |z|  = sqrt 5

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