if x-iy=underroot [(a-ib)/(c-id)]

prove that(x²+y²)²= a²+b²/c²+d2

Find the value of a for which one root of the quadratic equation (a²-5a+3)x²+(3a-1)x+2=0 is twice as large as the other.How can we eliminate alpha here? Please solve the problem?

Solve :- 2x² - (3+7i) x - (3-9i) = 0

ANURAG.

if (x+iy)(2-3i)=4+i then find (x,y)

If x + iy = a + ib/a- ib, show that x²+y²=1

Solve :- x² -(7 - i) x + (18 - i) = 0 over C.

ANURAG.

If x = 2 + 2^2/3+ 2^1/3, then find the value of x³ - 6x² + 6x.

if Z is a complex number such that Z-1 / Z+1 is purely imaginary.prove that |Z|=1

if the sum of the roots of the equation ax2 + bx + c = 0 is equal to the sum of the squares of their squares of their reciprocals , then show that bc² , ca² , ab² are in A.P.

if a² + b² =1 , then find the value of 1+b+ia/1+b-ia

if a is not equal to b and a^2=5a -3 , b^2=5b-3, then form the equation whose roots are a/b and b/a

let alpha and beta are the roots of x²-6x-2=0,with alpha beta . if a_n=alphaⁿ-betaⁿ for n=(greater than or equal to one)1,then value of a₁₀-2a₈/ 2a₉ is??

if a+ib= c+i / c-i , where c is real part

prove that

a square + b square =1

and b / a =2c / c square-1

 Q. If p+iq = (a-i)² / 2a-i , show that p²+q² = (a²+1)² / 4a²+1.