Question

PLEASE HURRY!!!

Let z = Equals 38 (cosine (StartFraction pi over 8 EndFraction) + I sine (StartFraction pi Over 8 EndFraction) ) and w = 2 (cosine (StartFraction pi Over 16 EndFraction) + I sine (StartFraction pi Over 16 EndFraction) ) .

What is the product of zw?
40 (cosine (StartFraction pi Over 16 EndFraction) + I sine (StartFraction pi Over 16 EndFraction) )
76 (cosine (StartFraction pi Over 16 EndFraction) + I sine (StartFraction pi Over 16 EndFraction) )
40 (cosine (StartFraction 3 pi Over 16 EndFraction) + I sine (StartFraction 3 pi Over 16 EndFraction) )
76 (cosine (StartFraction 3 pi Over 16 EndFraction) + I sine (StartFraction 3 pi Over 16 EndFraction) )

Answer 1

9514 1404 393

Answer:

d. 76(cos(3π/16) +i·sin(3π/16))

Explanation:

To form the product of 38cis(π/8) and 2cis(π/16), multiply the magnitudes and add the angles:

38cis(π/8) × 2cis(π/16) = (38×2)cis(π/8 +π/16) = 76cis(3π/16)

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In this context, a·cis(b) ≡ a(cos(b) +i·sin(b))