Question

How do you perform the operation in trigonometric form `(3/4(cos(pi/3)+isin(pi/3))(4(cos((3pi)/4)+isin((3pi)/4))`?

Answer 1

You multiply the magnitudes and add the angles: `(A(cos(theta) + isin(theta))(B(cos(phi) +isin(phi))) = AB(cos(theta+phi) + isin(theta+phi))`

Explanation:

Multiply the `3/4` and the `4`:

`3/4 4 = 3`

Add the angles:

`(3pi)/4 + pi/3 = (13pi)/12`

The answer is:

`3(cos((13pi)/12) + isin((13pi)/12))`