Final answer:
To identify the locations of the remaining 3 zeros, we use the fact that the system's impulse response is real-valued, implying conjugate symmetry. The three additional zeros would be the complex conjugate and the negatives of the given zero and its conjugate.
Step-by-step explanation:
To determine the locations of the other 3 zeros of the system function H(z) of a discrete-time LTI system with given properties, we need to understand the conjugate symmetry of poles and zeros in the z-plane. Since the given zero is complex and the impulse response is real-valued, we know that there must be a complex conjugate zero to preserve this real-valued property. Having 4 poles at z = 0.1 indicates a 4th order system.
Given the location of one zero at z = 1/√2ʲπ /⁴, and assuming the symmetry, the three remaining zeros must be located at the complex conjugates and the negatives of these values to maintain the system's stability and causality. Thus, the other zeros are likely at the conjugate of the given zero, and the negatives of both the given zero and its conjugate. This would imply, without giving specific numerical values as they're not provided, that the zeros form a symmetrical pattern centered around the origin of the z-plane.