To find the argument of a complex number, follow these simple steps:

1. Identify the Complex Number: A complex number looks like this:
   ( z = a + bi )
   Here, ( a ) is the real part, and ( b ) is the imaginary part.

2. Use the Tangent Function: You can find the argument ( \theta ) with this formula:
   ( \theta = \tan^{-1}\left(\frac{b}{a}\right) )
   In this formula, ( b ) is the vertical part, and ( a ) is the horizontal part.

3. Determine the Correct Quadrant: Depending on whether ( a ) and ( b ) are positive or negative, you may need to change ( \theta ):

   • If ( a > 0 ) and ( b > 0 ), ( \theta ) is in the first quadrant.
   • If ( a < 0 ), add ( 180^\circ ) (or ( \pi ) radians).
   • If ( a > 0 ) and ( b < 0 ), subtract from ( 360^\circ ) (or adjust accordingly in radians).

Example:
Take ( z = 3 + 4i ).
To find the argument, use:
( \theta = \tan^{-1}\left(\frac{4}{3}\right) \approx 53.13^\circ )

This information helps when you want to change the complex number into polar form. In polar form, the complex number looks like this:
( z = m(\cos \theta + i \sin \theta) ).