Let (z=x+y i ), where, (x, y ) are integers and (i= -1 ) the area of the rectangle whose vertices are the roots of the equation ( z z^3+z( z )^3=700 ) is

Step-by-step solution

It is given, for a complex number (z=x+i y ), where (x, y ) are integers such that ( aligned & z z^3+z( Z )^3=350 & Z Z (z^2+( ( )^2 )=350 & (x^2+y^2 ) 2 (x^2-y^2 )=350 [ z z =|z|^2 ] & (x^2+y^2 ) (x^2-y^2 )=175 & x^2+y^2=25 and & x^2-y^2=7 [ x, y Integer ] aligned ) So, (x^2=16 and y^2=9 ) Therefore vertices of the rectangle are (( 4, 3) ), so area of the rectangle is (4 4 3=48 ). Hence, option (c) is correct.