"DC" Impedances seen looking into terminals of a BJT
It’s all about Ohm’s law. The voltage at the base is

$$V_b = R_e I_e + V_{be} = I_b (\beta + 1) R_e + V_{be}.$$

Hence

$$R_b = \frac{V_b}{I_b} = (\beta + 1) R_e + \frac{V_{be}}{I_c / (\beta + 1)} = (\beta + 1)(R_e + R_{be}).$$

Since \$\beta\$ is large, the resistance looking into the base will be large as well.