Let (-2- 1 3 )^3= x+ i y 27 , i = -1 , where x and y are real numbers, then (y-x) has the value

Step-by-step solution

aligned & (-2- 1 3 i )^3= x+ i y 27 & (-2- 1 3 i )^3= 1 27 (-6- i )^3 & Consider, (-6- i )^3 & =(-6)^3+3(-6)^2(- i )+3(-6)(- i )^2+(- i )^3 & =-216-108 i +18+ i & =-198-107 i & (-2- 1 3 i )^3= -198-107 i 27 aligned Comparing with x+i y 27 , we get aligned & x=-198, y=-107 & y-x=-107+198=91 aligned