Question

If z₁ = 2 – i, z₂ = 1 + i

1. Find | z₁ + z₂ + 1| and |z₁ – z₂ + i| 

2. Hence find \(|\frac{z_1 + z_2+1}{z_1 - z_2 + i}|\)

Answer 1

1. |z₁ + z₂ + 1| = |2 – i + 1 + i + 1| = 4
|z₁ – z₂ + i| = |2 – i – 1 – i + i| = |1 – i|

 = \(\sqrt{1+1} = \sqrt{2}\)

2. \(|\frac{z_1 + z_2+1}{z_1 - z_2 + i}|\) = \(|\frac{z_1 + z_2+1}{z_1 - z_2 + i}|\) = \(\frac{4}{\sqrt 2}\) = 2\(\sqrt 2\)