If z=x+i y, z^ 1 / 3 =a-i b, then x a - y b =k (a²-b² ) where k is equal to

Step-by-step solution

z^ 1 / 3 =a-i b z=(a-i b)³ x+i y=a³+i b³-3 i a² b-3 a b² x=a³-3 a b² x a =a²-3 b² and y=b³-3 a² b y b =b²-3 a² So, x a - y b =4 (a²-b² )