To find the argument of the complex number \( z = \sqrt{3} + i \), we can use the formula for the argument:

\[
\text{arg}(z) = \tan^{-1}\left(\frac{y}{x}\right)
\]

where \( x \) is the real part and \( y \) is the imaginary part of the complex number. Here, \( x = \sqrt{3} \) and \( y = 1 \).

Calculating the argument:

\[
\text{arg}(z) = \tan^{-1}\left(\frac{1}{\sqrt{3}}\right)
\]

Since \( \tan\left(\frac{\pi}{6}\right) = \frac{1}{\sqrt{3}} \), we find:

\[
\text{arg}(z) = \frac{\pi}{6}
\]

Thus, the argument of \( \sqrt{3} + i \) is \( \frac{\pi}{6} \) radians.

### Do you want more details or have any questions?

Here are some related questions you might consider:
1. What is the modulus of the complex number \( \sqrt{3} + i \)?
2. How do you convert this complex number to polar form?
3. What is the geometric representation of \( \sqrt{3} + i \) in the complex plane?
4. How would the argument change if the imaginary part were negative?
5. Can you explain the significance of the argument in complex analysis?

**Tip:** Always remember that the argument is the angle formed with the positive x-axis in the complex plane.

Learn how to find the argument of the complex number sqrt(3) + i. This solution demonstrates how to calculate the argument using the inverse tangent function with the complex number's real and imaginary parts. Suitable for high school students in Grades 10-12.

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