Let

S = {z ∈ C : 4z² + z = 0}

Find:

Σ|z|²

Solution:

Equation:

4z² + z = 0

z(4z + 1) = 0

Roots:

z = 0 and z = −1/4

Now,

Σ|z|²

= |0|² + |−1/4|²

= 0 + 1/16

= 1/16

Answer: 1/16