w = √2 (cos(π/4) + i sin(π/4)) = √2 (1/√2 + i/√2) = 1 + i
z = 2 (cos(π/2) + i sin(π/2)) = 2i
Then
w - z = (1 + i) - 2i = 1 - i
so that
|w - z| = √(1² + (-1)²) = √2
and
arg(w - z) = -π/4
In polar form, we have
w - z = √2 (cos(-π/4) + i sin(-π/4)) = √2 (cos(π/4) - i sin(π/4))
