Perform the indicated math on the two vectors: (23, 13) minus (34∠-37°)

The vector (34, <-37) has horizontal and vertical components.

The horizontal component adds to the x-component of the first
vector, and the vertical component adds to the y-component of
the first vector.

The horizontal component of (34, <-37) is  34cos(-37)  =  27.15

The vertical component of  (34,  <-37) is  34sin(-37)  =  -20.46

The sum of the two horizontal components is (23 + 27.15)  = 50.15 

The sum of the two vertical components is  (13 - 20.46) =  -7.46 .

The sum of the two vectors is the vector   (50.15,  -7.46) . 

From negative to negative