Using the vectorial representation of complex numbers it is possible to get some interesting inequalities.

(a) Is it true that for a complex number z = x + jy we have that ∣x∣ ≤ ∣z∣? Show it geometrically by representing z as a vector.

(b) The so called triangle inequality says that for any complex (or real) numbers z and v we have that ∣z + v∣ ≤ ∣z∣ + ∣v∣. Show this geometrically.

(c) If z = 1 + jand v = 2 + jis it true that

(i) |z + v| ≤ |z| + |v|?    (ii) |z − v| ≤ |z| + |v|?