To calculate the magnitude of the vector \(\mathbf{a} = 4\mathbf{i} + 3\mathbf{j}\), you can use the formula for the magnitude of a vector in two dimensions:
\[ |\mathbf{a}| = \sqrt{x^2 + y^2} \]
In this case, \(x = 4\) and \(y = 3\). Plugging in the values:
\[ |\mathbf{a}| = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \]
Thus, the magnitude of the vector \(\mathbf{a}\) is \(5\).