University-数学讨论区-Linear Algebra, Advanced Algebra

Ivanlsy

原帖由 yw46 于 11-8-2009 05:57 PM 发表
ivanlsy.wordpress.com

The authors have deleted this blog. The content is no longer available.
看不到

哦对了~
因为我没有时间去经营他~
所以我就关闭了~
add我MSN吧~

eric336

let z=x+iy
prove that |z| < |x| + |y| < √2 |z|

这题要怎样prove呢？

dunwan2tellu

原帖由 eric336 于 4-11-2009 02:18 AM 发表
let z=x+iy
prove that |z| < |x| + |y| < √2 |z|

这题要怎样prove呢？

|z| = |x + iy| =< |x| + |iy| = |x| + |y|  (triangle inequality)

√2 |z| = √[2 (x^2 + y^2) ] >= √(x^2 + y^2 + 2|xy|) = √(|x|+|y|)^2 = |x| + |y|   ( x^2 + y^2 >= 2|xy|)