RU-ALLRUSSIAN 1976 Problem 6

a, b, c, d are vectors in the plane such that $\mathbf{a} + \mathbf{b} + \mathbf{c} + \mathbf{d} = 0$ . Show that $\left|\mathbf{a}\right| + \left|\mathbf{b}\right| + \left|\mathbf{c}\right| + \left|\mathbf{d}\right|\geq \left|\mathbf{a}\right|$ $+\mathbf{d}\mathbf{i} + \mathbf{i}\mathbf{b} + \mathbf{d}\mathbf{i} + \mathbf{i}\mathbf{c} + \mathbf{d}\mathbf{i}$ .