What is norm complex number?

A norm complex number is a complex number that has a magnitude or length associated with it. This magnitude or length is called the norm of the complex number and is represented by |z| where z is the complex number. The norm is defined as the square root of the sum of the squares of the real and imaginary parts of the complex number.

For example, if z = 3 + 4i, then the norm of z is |z| = √(3² + 4²) = √25 = 5.

The concept of a norm is important in complex analysis and vector calculus. It allows us to measure and compare the sizes of complex numbers, just as we measure distances between points in Euclidean space. The norm satisfies several properties, such as being non-negative, being zero if and only if the complex number is zero, and satisfying the triangle inequality.

In addition, the norm also has the property that it is multiplicative, meaning that |zw| = |z| |w| for any two complex numbers z and w. This property allows us to simplify complex calculations involving multiplication by reducing them to simple algebraic manipulations involving the norms of the complex numbers involved.