已知复数Z1=cosA-i,Z2=sinA+i,求Z1*Z2的模的最大值

问题描述:

已知复数Z1=cosA-i,Z2=sinA+i,求Z1*Z2的模的最大值

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)^2max |z1.z2|^2 = 2+1/4 = 9/4max |z1.z2|=3/...