Answer:
The product of
36√cis(π/8) and 25√cis(7π/6)
is
(225√2)√[√(2 + √2) + i√(2 - √2)][√(3(-1 + i))]
Step-by-step explanation:
First note that
cis(π/8) = cos(π/8) + isin(π/8)
cis(7π/6) = cos(7π/6) + isin(7π/6)
cos(π/8) = (1/2)√(2 + √2)
sin(π/8) = (1/2)√(2 - √2)
36√cis(π/8) = (36/√2)√[√(2 + √2) + i√(2 - √2)]
cos(7π/6) = -(1/2)√3
sin(7π/6) = (1/2)√3
25√cis(7π/6) = (25/2)√3(-1 + i)
The product,
36√cis(π/8) × 25√cis(7π/6)
= (36/√2)√[√(2 + √2) + i√(2 - √2)] × (25/2)√3(-1 + i)
= (225√2)√[√(2 + √2) + i√(2 - √2)][√(3(-1 + i))]
