For the complex number 3 + 4i, what is the absolute value and the argument? Is it not tan (4/3)?

The absolute value of any number, including complex
numbers, is its distance from zero.

You may be confusing
the unit circle, which is the general idea for the absolute value of a complex number,
with the trigonometry of the unit circle.

But the absolute
value uses the Pythagorean theorem: the real number is plotted on the x-axis, and the
imaginary number on the y-axis.  So to get the distance from the plotted complex number
to zero would be the square root of the units on the x-axis squared plus the units on
the y-axis squared:

sqrt (9+16) = sqrt 25 =
5.

You can think of the tangent as the slope of the
hypotenuse of the right triangle, or sine/cosine.  But it's not absolute
value...