Find the modulus and argument of the number

Question

Z= -sin(π/8) - i cos(π/8)

Answer 1

sinπ/8 = cos 3π/8 and vice-versa, so you have
-cos(3π/8) - i sin(3π/8) = -1 cis(3π/8)
so modulus = -1
argument = 3π/8