[代數][謝謝老師]

[LATEX]

複數

[thepiano]

|z^3 - 3z - 2|
=|z + 1||z + 1||z - 2|

最大值出現在 |z + 1| = |z - 2|

令 z = x + yi
(x + 1)^2 + y^2 = (x - 2)^2 + y^2
x = 1/2

又 x^2 + y^2 = 1
y = ±√3 / 2

z = (1 ± √3i)/2

所求 = |z + 1|^3 = 3√3