How do you multiply (7(cos 23+isin 23)) (4(cos 7+isin 7))?

1 Answer
Douglas K.
May 17, 2018

Given: (7(cos(23)+isin(23))) (4(cos(7)+isin(7)))(7(cos(23)+isin(23)))(4(cos(7)+isin(7)))

7 is the magnitude of the first factor and 4 is the magnitude of the second factor.

I multiply the magnitudes:

7(4) = 287(4)=28

2323 is the angle of the first factor and 77 is the angle of the second factor.

I add the angles:

23+7 = 3023+7=30

This the process for multiplication in the trigonometric form:

(7(cos(23)+isin(23))) (4(cos(7)+isin(7)))= 28(cos(30)+isin(30))(7(cos(23)+isin(23)))(4(cos(7)+isin(7)))=28(cos(30)+isin(30))

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