[" If "a+ib=(c+i)/(c-i)," prove that "a^(2)+b^(2)=1" and "(b)/(a)=(2c)/(c^(2)-1)],[" OR "]

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+ 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 a + ib = (1 + i) / (1 - i) , prove that a^2 + b^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+ib)= (1+i ) /(1-i) , then prove that (a ^2+b^ 2 )=1

(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,b,c,d are in G.P.prove that: (i) quad (a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P. (i) (1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P.

If (a+ib)/(c+id)=x+iy, 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)