Let w 1 be the point obtained by the rotation of z 1 = 5 + 4 i about the origin through a right angle in the anticlockwise direction, and w 2 be the point obtained by the rotation of z 2 = 3 + 5 i about the origin through a right angle in the clockwise direction. Then the principal argument w 1 - w 2 is equal to

Step-by-step solution

Given, Two complex numbers w 1   &   w 2 w 1 = 3 + 5 i and w 2 = 5 + 4 i are both rotated by 90 ° with respect to origin anticlock-wise and clockwise respectively, So by concept of rotation we get, w 3 = i w 1 = i 3 + 5 i = - 5 + 3 i And w 4 = - i w 2 = - i 5 + 4 i = 4 - 5 i Now principal argument of w 3 - w 4 = - 9 + 8 i will be π - tan - 1 8 9 as complex number is in second quadrant so principal argument is given by π - tan - 1 y x