[" 9.If "x+y=(x-ib)/(a-ib)" ,prove that "x^(2)+y^(2)=1],[" 9.Find the least positve integral value of nfor which "((1+i)/(1-i))^(n)" is real."],[" 10.Find the real values of for which the complex number "(1+i cos theta)/(1-2i cos theta)" is purely real."],[" 1.Find the smallest positive integer value of nfor which "((1+i)^(n))/((1-t)^(n-2))" is a real number."],[[" 12.If "((1+i)/(1-i))^(3)-((1-i)/(1+i))^(3)=x+iy," find "(x,y)," (NCERTEXEMPLARI) "],[" I3.If "((1+i)^(2))/(2-i)=x+iy," find "x+y.]]