Find the product below Leave the result in polar form 7cos 1

Find the product below. Leave the result in polar form. [7(cos 110 degree + j sin 110 degree)] [2(cos 40 degree + j sin 40 degree)] What is the product? (cos degree + j sin degree) (Simplify your answers. Type integers or decimals. Use angle measures greater than or equal to 0 and less than 360.)

Solution

let x = 7cos(110) and y = 7sin(110) then x + jy =7cos(110) + j 7sin(110) = 7 e^j110

let a = 2cos(40) and b = 2sin(40) then a + jb = 2cos(40) + j 2sin(40) = 2e^j40

Now consider

[ 7(cos(110) + j sin(110)) ][2( cos(40) + j 2sin(40) = 7 e^j110   x 2e^j40 = 14e^{j(40+ 110)} = 14e^j150

Thus , the required product is 14[ cos(150 ) + j sin( 150 ) ]