Question -
Answer -
Given:
[(1 +i)/(1 – i)] – [(1 – i)/(1 + i)]
So,
Z = [(1 + i)/(1 – i)]– [(1 – i)/(1 + i)]
Let us simplify, weget
= [(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
We know that for acomplex number Z = (a+ib) it’s magnitude is given by |z| = √(a2 + b2)
So,
|Z| = √(02 + 22)
= 2
∴ The modulus of [(1 +i)/(1 – i)] – [(1 – i)/(1 + i)] is 2.