How to calculate the argument of a complex number?

To calculate the argument of a complex number, use the formula arg(z) = tan^-1 (Im(z)/Re(z)).

The argument of a complex number is the angle between the positive real axis and the line joining the origin to the complex number in the complex plane. It is measured in radians and can be calculated using the formula arg(z) = tan^-1 (Im(z)/Re(z)), where Im(z) is the imaginary part of the complex number and Re(z) is the real part of the complex number.

For example, let z = 3 + 4i. The real part of z is 3 and the imaginary part of z is 4. Therefore, arg(z) = tan^-1 (4/3) = 0.93 radians (to 2 decimal places).

It is important to note that the argument of a complex number is not unique, as it can differ by multiples of 2π. To find all possible arguments of a complex number, add or subtract multiples of 2π to the calculated argument.

For example, if arg(z) = 0.93 radians, then arg(z) + 2π = 3.07 radians is also a possible argument of z.

In summary, the argument of a complex number can be calculated using the formula arg(z) = tan^-1 (Im(z)/Re(z)). It is measured in radians and can have multiple possible values differing by multiples of 2π.