Question

Find the modulus of [(1 + i)/(1 – i)] – [(1 – i)/(1 + i)]

Answer 1

Given as

[(1 + i)/(1 – i)] – [(1 – i)/(1 + i)]

Therefore,

Z = [(1 + i)/(1 – i)] – [(1 – i)/(1 + i)]

Now let us simplify, we get

= [(1 + i) (1 + i) – (1 - i) (1 - i)]/(1² – i²)

= [1² + i² + 2(1)(i) – (1² + i² – 2(1)(i))]/(1 – (-1)) [Since, i² = -1]

= 4i/2

= 2i

As we know that for a complex number Z = (a + ib) it’s magnitude is given by |z| = √(a² + b²)

Therefore,

|Z| = √(0² + 2²)

= 2

Thus, the modulus of [(1 + i)/(1 – i)] – [(1 – i)/(1 + i)] is 2.