Question

The modulus of \(\rm {1\ -\ i\over1\ +\ i}-{1\ +\ i\over1\ -\ i}\)
1. 1
2. 2
3. 3
4. 4

Answer 1

Correct Answer - Option 2 : 2

Concept:

The modulus of a complex number z = x + iy

|z| = \(\rm \sqrt{x^2+y^2}\)

Calculation:

z = \(\rm {1\ -\ i\over1\ +\ i}-{1\ +\ i\over1\ -\ i}\)

z = \(\rm {(1\ -\ i)^2-(1\ +\ i)^2\over(1\ +\ i)(1\ - \ i)}\)

z = \(\rm {(1\ -\ 2i\ -\ 1)-(1\ +\ 2i\ -\ 1)\over(1^2\ -\ i^2)}\)

z = \(\rm -2i\ -\ 2i\over2\)

z = -2i

Now |z| = \(\rm \sqrt{0^2+(-2)^2}\)

|z| = 2