MathDB

For

k=1,2 \dots, n

let

z_k=x_k+iy_k,

where the

x_k

and

y_k

are real and

i=\sqrt{-1}

. Let

r

bet the absolute value of the real part of

\pm \sqrt{z_1^2+z_2^2+\dots z_n^2}.

Prove that

r\leq |x_1|+|x_2|+ \dots +|x_n|.

B6