The radius of the circle represented by ( 1 + i ) ( 1 + 3   i ) ( 1 + 7   i ) = x + i y is ( i = -…

The radius of the circle represented by $(1+i)(1+3 i)(1+7 i)=x+iy$ 

$( 1+ 3i^2 + 4i)(1 + 7i) = x + iy$

$1+ 3i^{2 }+ 4i + 7i + 21i^3 + 28i^2 = -30-10i = x + iy$

$x=-30 , y=-10$

Radius of circle :

$\sqrt{(x^2+y^2)} = \sqrt{{30}^2+{10}^2} = \sqrt{900+100}$$= \sqrt{1000} = 10\sqrt{10}$ .