38. Among the complex numbers $Z$, satisfying the condition $|Z-25 i| \leqslant 15$, find the number with the smallest argument. Make a drawing.
38. The modulus of the difference of two complex numbers $\left|z_{1}-z_{2}\right|$ is equal to the distance between the corresponding points in the complex plane. The condition $|z-25 i|<15$ is satisfied by points in the complex plane lying inside and on the boundary of a circle with center at the point $z_{0}=25 i$ and radius 15. The number with the smallest argument corresponds to the point $z_{1}$, where the line drawn from the origin is tangent to the circle. From the right triangle $O z_{0} z_{1}$, we find $x_{1}=12, y_{1}=16, z_{1}=12+16 i$.