he Modulus of a Complex Number Definition: The modulus or absolute value of a complex number z= a + bi is its distance from the origin on the complex plane, that is, 121 = Vo? + b2 = (Re(z))2 + (Im(z)(= VZ) In particular, the modulus | | of a complex number z is always a real number. Im 2 = a + bi b (Pythagoras' Theorem) 121 = a2 + b2 Re Note: zz = 1212 Example: ? X | -5+61) = Vi+5)2 +62 14 + 7i] = ? x 1-1 – 211 = ? X