Find the argument of \( \frac{3}{5}+\frac{4 i}{5} \)

To find the argument of the complex number \( z = \frac{3}{5} + \frac{4i}{5} \), we can use the formula for the argument of a complex number, which is given by \( \tan^{-1} \left(\frac{b}{a}\right) \), where \( a \) is the real part and \( b \) is the imaginary part. Here, \( a = \frac{3}{5} \) and \( b = \frac{4}{5} \). First, we compute the ratio: \[ \frac{b}{a} = \frac{\frac{4}{5}}{\frac{3}{5}} = \frac{4}{3} \] Now, we find the angle whose tangent is \( \frac{4}{3} \): \[ \theta = \tan^{-1} \left(\frac{4}{3}\right) \] The argument of the complex number is therefore: \[ \text{arg}(z) = \tan^{-1} \left(\frac{4}{3}\right) \] This angle is in the first quadrant since both the real and imaginary parts are positive. Hence, the argument is simply: \[ \text{arg}(z) \approx 0.93 \text{ radians} \text{ or } 53.13^\circ \]