Given v 7 7 squareroot 3 find the magnitude and direction a

Given v = (-7, 7 squareroot 3), find the magnitude and direction angle of vector v. Find the exact value of the product and write the result in a + ib form: 7(cos (120 degree) + i sin (120 degree)) 3 (cos (30 degree) + i sin (30 degree))

Solution

a) v = <-7, 73 >

Magnitude = v = sqrt[(-7)^2 + (73)^2] = 14

direction = arctan(-73/7) = -60 degree

b) 7(cos120 + i*sin120)*3(cos30 + i*sin30) = 21*(cos150 + i*sin150) = 21(-0.866 + i*0.5)