Let z=x+i y be a complex number, where x and y are integers. Then, the area of the rectangle whose vertices are the roots of the equation z z ^3+ z z^3=350 is

Step-by-step solution

Since, z z (z^2+ z ^2 )=250 aligned & 2 (x^2+y^2 ) (x^2-y^2 )=350 & (x^2+y^2 ) (x^2-y^2 )=175 aligned Since, x, y I , the only possible case which gives integral solution, is and aligned x^2+y^2 & =25 x^2-y^2 & =7 aligned From Eqs. (i) and (ii), we get x^2=16 ; y^2=9 x= 4 ; y= 3 Area of rectangle =8 6=48