Z=cosθ+isinθ 求u=1-i+Z的模

题目

Z=cosθ+isinθ 求u=1-i+Z的模

答案

u = (1 + cosθ) + i (sinθ - 1)
|u| = [(1 + cosθ)^2 + (sinθ - 1)^2]^0.5
= [1 + 2 cosθ + cos^2θ + 1 - 2 sinθ + sin^2θ]
= √[3 + 2 (cosθ - sinθ)]