Complex Numbers and De Moivre’s Theorem

A number of the form \(z

A number of the form \(z = a + bi\), where \(a\) and \(b\) are real numbers and \(i = \sqrt{-1}\). Here, \(a\) is the real part and \(b\) is the imagi

Defined as \(i = \sqrt{

Defined as \(i = \sqrt{-1}\), so \(i^2 = -1\). Higher powers of \(i\) repeat in a cycle: \(i, -1, -i, 1\).

For \(z = a + bi\)

For \(z = a + bi\), the conjugate is \(ar{z} = a - bi\). It helps in division and finding modulus.

The modulus \(|z| = \sqrt{a^2 +

The modulus \(|z| = \sqrt{a^2 + b^2}\) is the distance from origin to point \(P(a,b)\). The argument \(\arg(z) = an^{-1}(b/a)\) is the angle with the

A complex number can be written

A complex number can be written as \(z = r(\cos heta + i\sin heta)\), where \(r = |z|\) and \( heta = \arg(z)\).