To find the absolute value of a complex number, I need to find its modulus, which is the distance from the origin in the complex plane. I can write \[1 + \sqrt{3}i = 2e^{\frac{\pi}{3}i}\] using Euler's formula, since the modulus is 2 and the argument is \(\frac{\pi}{3}\). Then, using the properties of exponents, I can write \[\left(1 + \sqrt{3}i\right)^4 = 2^4e^{4\cdot\frac{\pi}{3}i}\] Therefore, the absolute value of \[\left(1 + \sqrt{3}i\right)^4\] is 16. 
Find \[\left|\left(1 + \sqrt{3}i\right)^4\right|\]