For any integer \( k \), \( i^{4k}=1,\)\( i{4k + 1}=i\), \(i^{4k + 2}= – 1,\) \(i{4k + 3} = – i \)

The conjugate of the complex number \( z = a + ib\), denoted by z , is given by \( z = a – ib\).

The polar form of the complex number \( z = x + iy\) is \(r (\cos θ + i \sin θ)\), where \(r = \sqrt{x^2 + y^2} \) (the modulus of z) and \( \cos θ = \frac{x}{r} \), \(\sin θ = \frac{y}{r}\). (θ is known as the argument of z. The value of θ, such that – π < θ ≤ π, is called the principal argument of z.

A polynomial equation of *n* degree has *n* roots.

The solutions of the quadratic equation \(ax^2 + bx + c = 0\), where a, b, c ∈ R, a ≠ 0, \( b^2 – 4ac < 0 \), are given by \( x = \frac{− b \pm \sqrt{4ac – b2} i}{2a} \).