Properties of Modulus, amplitude and conjugate of complex numbers

• The modulus of a complex number is always non-negative, and is zero if and only if the complex number is zero.
• The modulus of a complex number satisfies the triangle inequality, which states that the modulus of the sum of two complex numbers is less than or equal to the sum of their individual moduli.
• The amplitude of a complex number is not unique, as adding or subtracting a multiple of 2π to the amplitude produces an equivalent angle.
• The amplitude of the product of two complex numbers is the sum of their individual amplitudes, while the amplitude of the quotient of two complex numbers is the difference of their individual amplitudes.
• The conjugate of a complex number is obtained by reflecting the number about the real axis, and has the same modulus as the original number.