" 32.If "a+ib=(c+i)/(c-i')" where "c" is real,Prove "a^(2)+b^(2)=1" and "(b)/(a)=(2c)/(c^(2)-1)

If a+ib=(c+i)/(c-i), where c is real,prove that: a^(2)+b^(2)=1 and (b)/(a)=(2c)/(c^(2)-1)

If a+ib= (c+i)/(c-i) , where c is real, prove that a^2+b^2=1 and b/a= (2c)/(c^2-1) .

If a+i b=(c+i)/(c-i) , where c is real, prove that: a^2+b^2=1 and b/a=(2c)/(c^2-1)dot

If a+ bi = (c + i)/(c-i), a, b , c in R , show that a^(2) + b^(2)=1 and (b)/(a)= (2c)/(c^(2)-1)

If (c+i)/(c-i)= a+ ib , where a, b, c are real, then a^2+ b^2 equals :

if a,b,c,a_(1),b_(1) and c_(1) are non-zero complexnumbers satisfying (a)/(a_(1))+(b)/(b_(1))+(c)/(c_(1))=1+i and (a_(1))/(a)+(b_(1))/(b)+(c_(1))/(c)=0 where i=sqrt(-1) ,the value of (a^(2))/(a_(1)^(2))+(b^(2))/(b_(1)^(2))+(c^(2))/(c_(1)^(2)) is

(i) If x-iy = sqrt((a-ib)/(c-id)) prove that (x^(2) + y^(2)) =(a^(2) + b^(2))/(c^(2) + d^(2))

If (a+ib)/(c+id)=x+i y , prove that(i) (a-ib)/(c-id)=(x-iy) (ii) (a^2+b^2)/(c^2+d^2)=(x^2+y^2)

If (a+ib)/(c+id)=x+i y , prove that(i) (a-ib)/(c-id)=(x-iy) (ii) (a^2+b^2)/(c^2+d^2)=(x^2+y^2)

Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)