If z1 = 2 – i, z2 = 1 + i, find |{z_1+z_2+1}{z_1-z_2+1}

Given, z₁ = 2 – i, z₂ = 1 + i

\( | \dfrac{z_1+z_2+1}{z_1-z_2+1}|\)

\( | \dfrac{(2-i)+(1+i)+1}{(2-i)-(1+i)+1}|\)

= \( | \dfrac{4}{2-2i}|\)

= \( | \dfrac{4}{2(1-i)}|\)

= \( | \dfrac{2}{1-i}\times \dfrac{1+i}{1+i}|\)

= \( | \dfrac{2(1+i)}{(1^2-i^2)}|\)

= \( | \dfrac{2(1+i)}{1+1}|\)

= \( | \dfrac{2(1+i)}{2}|\)

= \( |1+i|=\sqrt{1^2+1^2}\)

\( =\sqrt{2}\)