precalculus

After some extremely long computations, |w| works out to 2.

|w| = 1

We don't even need to know the value of z! Absolutely unnecessary information!

|w|^2 = w(cong(w))

Multiplying the conjugate of w in the second equation by the value of w given in the second equation. This gives us |w|^2 = 1

|w| = 1 as magnitudes are always nonnegative.