Question

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

Answer 1

Given: `(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) = 28`

`23` is the angle of the first factor and `7` is the angle of the second factor.

I add the angles:

`23+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))`