Tunjukkan bahwa z + 1 + 1 + z + z ^ 2 + 1 + z ^ 3> = 1?

# | z + 1 | + | z ^ 2 + z + 1 |> = | (z ^ 2 + z + 1) - (z + 1) | = | z ^ 2 | = | z | ^ 2> = 1 #

# | z + 1 | + | z ^ 2 + z + 1 |> = | z || z + 1 | + | z ^ 2 + z + 1 | = #

# | z (z + 1) | + | z ^ 2 + z + 1 | = | z ^ 2 + z | + | z ^ 2 + z + 1 |> = | (z ^ 2 + z + 1) - (z ^ 2 + z) | = 1 #

Karenanya, # | z + 1 | + | 1 + z + z ^ 2 |> = 1 #, # z ##di## CC #

dan

# | z + 1 | + | 1 + z + z ^ 2 | + | 1 + z ^ 3 |> = | 1 + z | + | 1 + z + z ^ 2 |> = 1 #,

'#=#', # z = -1vvz = e ^ ((2k + 1) iπ) #, # k ##di## ZZ #