Final answer:
To find the product of complex numbers z and w, we multiply their magnitudes and add their angles.
Step-by-step explanation:
To find the product of zw, we need to multiply the given complex numbers. The product of two complex numbers is calculated by multiplying their magnitudes and adding their angles. Let's calculate:
z = 38 (cos(π/8) + i sin(π/8))
w = 2 (cos(π/16) + i sin(π/16))
Multiplying the magnitudes: |z| * |w| = 38 * 2 = 76
Adding the angles: arg(z) + arg(w) = π/8 + π/16 = 5π/16
So, zw = 76 (cos(5π/16) + i sin(5π/16))