1)
ч=π／4时,
Z = √2 + √2i = 2(√2/2 + √2/2i )
化成三角形式,得
Z = 2[cos(π/4)+sin(π/4)i]
2)
|Z|²
=(cosч-sinч+√2)^2+(cosч+sinч)^2
=(cosч-sinч)^2+(cosч+sinч)^2 + 2√2(cosч-sinч) + 2
=2[(cosч)^2+(sinч)^2] + 2√2(cosч-sinч) + 2
=2√2(cosч-sinч) + 4
=4sin(ч+3π/4)+4

所以 ,当 ч+3π/4 = π/2 + 2kπ 时,
即 ч = 2kπ - π/4 时,
|Z|取最大值 √(4+4) = 2√2 .