已知复数Z1=cosA-i, Z2=sinA+i, 求Z1*Z2的模的最大值

2025-06-28 09:09:12
推荐回答(1个)
回答1:

z1.z2
=(cosA-i)(sinA+i)
= sinAcosA+1+ (cosA-sinA)i
|z1.z2|^2
=(sinAcosA+1)^2+ (cosA-sinA)^2
=(sinAcosA)^2+2sinAcosA+1 + 1-2sinAcosA
=2+(sinAcosA)^2
=2+ (1/4)(sin2A)^2
max |z1.z2|^2 = 2+1/4 = 9/4
max |z1.z2|=3/2