Results On Moduli And Argument Of Complex Numbers
Complex Numbers of Class 11
Results on The Modulii of Complex Numbers
For any complex number z1, z2 and z the following can be easily concluded.
(a) |z| = 0 ⇔ z = 0 ⇔ x = 0 and y = 0
(b) z
= |z|2
(c) |z1z2| = |z1| |z2|
(d) 
(e) |z1 + z2| ≤ |z1| + |z2|
(f) |z1 − z2| ≥ ||z1| − |z2||
RESULTS ON ARGUMENT OF A COMPLEX NUMBER
(a) arg(z1z2) = argz1 + argz2
(b) arg
= argz1 − argz2
(c) arg zn = n arg z
