Find the modulus of (1+i)/(1-i) - (1-i)/(1+i)

Solution:

(1+i)/(1-i) - (1-i)/(1+i) = (1+i)/(1-i) · (1+i) / (1+i) - (1-i)/(1+i) · (1-i) / (1-i)

= (1 + 2i + i²) / (1 - i²) - (1 - 2i + i²) / (1 - i²)

= (2i) / 2 - (-2i) / 2 (because i² = -1)

= i + i

= 2i

Its modulus is, √(0² + 2²) = 2

Thus, the modulus of (1+i)/(1-i) - (i-i)/(1+i) = 2

NCERT Solutions Class 11 Maths Chapter 5 Exercise ME Question 15

Find the modulus of (1+i)/(1-i) - (1-i)/(1+i)

Summary:

The modulus of (1+i)/(1-i) - (i-i)/(1+i) is 2