已知复数Z1=m+(4-m^2)*i (m属于R),和Z2=2cosa+(u+3sina)(u属于R),若Z1=Z2,证明:-9/16
问题描述:
已知复数Z1=m+(4-m^2)*i (m属于R),和Z2=2cosa+(u+3sina)(u属于R),
若Z1=Z2,证明:-9/16
答
z1=z2m = 2cosa 4 - m²= u + 3sina4 - u - 3sina = 4cos²au = 4sin²a - 3sina = (2sina - 3/4)² - 9/162sina - 3/4 ∈[-11/4,3/4](2sina - 3/4)²∈[0,121/16]故u∈[-9/16,7]