如题所述
第1个回答 2023-11-09
cosz=cos(x+iy)
=cosx*cosiy-sinx*siniy
=cosx*chy-isinxshy
于是 |cosz|=根号(cos^2xsh^y+sin^2xsh^2y)
=根号[(1-sin^2x)ch^2y+sin^2xsh^2y]
=根号[ch^2y-sin^2x(ch^2y-sin^2y)]
=根号(ch^2y-sin^2x) >=根号(ch^2y-1)
所以 |cosz|>=根号(ch^2y-1) =|shy|=|[e^y-e^(-y)]/2|
而上式右边当y->无穷时无限变大 可证明 cosz是无界的
=cosx*cosiy-sinx*siniy
=cosx*chy-isinxshy
于是 |cosz|=根号(cos^2xsh^y+sin^2xsh^2y)
=根号[(1-sin^2x)ch^2y+sin^2xsh^2y]
=根号[ch^2y-sin^2x(ch^2y-sin^2y)]
=根号(ch^2y-sin^2x) >=根号(ch^2y-1)
所以 |cosz|>=根号(ch^2y-1) =|shy|=|[e^y-e^(-y)]/2|
而上式右边当y->无穷时无限变大 可证明 cosz是无界的
