Question

If z₁ = 5 - 2i and z₂ = 3 + i, then `|(z_1 + z_2)/(z_1 - z_2)|` = ______ 

Options

• `sqrt(13/18)`

• `sqrt(1/5)`

• `sqrt(18/13)`

• `sqrt5`

Answer 1

If z₁ = 5 - 2i and z₂ = 3 + i, then `|(z_1 + z_2)/(z_1 - z_2)|` = `underline(sqrt5)`

Explanation:

z₁ + z₂ = 8 - i and z₁ - z₂ = 2 - 3i

∴ `(z_1 + z_2)/(z_1 - z_2) = (8 - i)/(2 - 3i) = 19/13 + 22/13i`

∴ `|(z_1 + z_2)/(z_1 - z_2)| = |19/13 + 22/13i| = sqrt((19/13)^2 + (22/13)^2)`

= `sqrt(845/169) = sqrt5`