If z₁ = 2 - i, z₂ = 1 + i, find |(z₁ + z₂ + 1)/ (z₁ - z₂ + 1)|

Solution: 

z₁ + z₂ + 1 = (2 - i) + (1 + i) + 1 = 4

z₁ - z₂ + 1 = (2 - i) - (1 + i) + 1 = 2 - 2i

(z₁ + z₂ + 1)/ (z₁ - z₂ + 1) = 4 / (2 - 2i)

= 2 / (1 - i)

= 2 (1 + i) / (1 + 1) (Rationalized the denominator)

= 1 + i

Now,

|(z₁ + z₂ + 1)/ (z₁ - z₂ + 1)| = √(1² + 1²) = √2.

Hence the value of |(z₁ + z₂ + 1)/ (z₁ - z₂ + 1)| is √2

NCERT Solutions Class 11 Maths Chapter 5 Exercise ME Question 10

If z₁ = 2 - i, z₂ = 1 + i, find |(z₁ + z₂ + 1)/ (z₁ - z₂ + 1)|

Summary:

Hence the value of |(z₁ + z₂ + 1)/ (z₁ - z₂ + 1)| is √2