[" 8.If "x+iy=(u+u)/(a-ib)," prove that "x^(2)+y^(2)=1],[" 9.Find the least positive integral value of "n" for which "((1+i)/(1-i))^(n)" is real."],[" 10.Find the real values of "theta" for which the complex number "(1+i cos theta)/(1-2i cos theta)" is purely real."],[" 11.Find the smallest positive integer value of "n" for which "((1+i)^(n))/((1-i)^(n-2))" is a real number."],[" 12.If "((1+i)/(1-i))^(3)-((1-i)/(1+i))^(3)=x+iy," find "(x,y)quad " [NCERTEXEMPLAR] "]