Complex Numbers

The imaginary unit i is defined

The imaginary unit i is defined as i = √(-1), which means i² = -1. This fundamental definition allows us to represent square roots of negative numbers

A complex number is expressed as

A complex number is expressed as z = a + bi, where a is the real part (Re(z) = a) and b is the imaginary part (Im(z) = b). Both a and b are real numbe

The conjugate of z =

The conjugate of z = a + bi is z̄ = a - bi. It's obtained by changing the sign of the imaginary part. For example, if z = 3 + 4i, then z̄ = 3 - 4i. Pr

The modulus of z =

The modulus of z = a + bi is |z| = √(a² + b²). It represents the distance of the complex number from the origin in the Argand Plane. For example, |3 +

The argument θ of z =

The argument θ of z = a + bi is the angle that the line OP (where P is the point representing z) makes with the positive x-axis. It's calculated as θ