Question

wu = 5 (cos (15") + i sin (15))w2 = 3 (cos (45') + i sin (45-))What is wi. W2?Choose 1 answer:15 (cos (60") + i sin (60))15 (cos (30") + i sin (30))8 (cos (30") + i sin (30))8 (cos (60") + i sin (60))

Answer 1

From the information given,

w1 = 5(cos(15) + isin(15))

w2 = 3(cos(45) + isin(45))

Let A represent 15 degrees and B represent 45 degrees

To find w1 * w2, we would multiply each term in the first parentheses by each term in the second parentheses. We have

w1 * w2 = 5(Cos(A) + iSin(A)) * 3(Cos(B) + iSin(B))]

= 15[CosACosB + CosA * iSinB + iSinACosB + i^2SinASinB]

= 15[CosACosB + i(CosASinB + SinACosB) + i^2SinASinB]

= 15[CosACosB + i(SinACosB + CosASinB) + i^2SinASinB]

Recall, i^2 = - 1

Thus, we have

15[CosACosB + i(CosASinB + SinACosB) - SinASinB]

15[CosACosB - SinASinB + i(SinACosB + CosASinB)]

Recall the following trigonometric identities

Cos(A + B) = CosACosB - SinASinB

Sin(A + B) = SinACosB + CosASinB

By applying these identities, we have

15[Cos(A + B) + i(Sin(A + B)]

By replacing A with 15 and B with 45, we have

15[Cos(15 + 45) + i(Sin(15 + 45)]

= 15[(Cos60 + iSin60]

Option 1 is correct