The distance (\(d\)) between two complex numbers \(z_1 = a_1 + b_1i\) and \(z_2 = a_2 + b_2i\) in the complex plane is given by the formula:
\[ d = \sqrt{(a_2 - a_1)^2 + (b_2 - b_1)^2} \]
For \(z_1 = 3 + 7i\) and \(z_2 = -5 - 2i\), the real parts are \(a_1 = 3\) and \(a_2 = -5\), and the imaginary parts are \(b_1 = 7\) and \(b_2 = -2\). Substitute these values into the distance formula:
\[ d = \sqrt{(-5 - 3)^2 + (-2 - 7)^2} \]
Calculate the values inside the square root, and then find the square root of the sum:
\[ d = \sqrt{(-8)^2 + (-9)^2} = \sqrt{64 + 81} = \sqrt{145} \]
Therefore, the distance between \(z_1\) and \(z_2\) is \(\sqrt{145}\).