If `i= sqrt(-1)`, prove that following `(x+1+ i) (x + 1- i) (x-1 + i) (x-1-i)= x^(4) + 4`

Prove that: x^4+4=(x+1+i)(x+1-i)(x-1+i)(x-1-i) .

Solve the following equations : (i) |x-2| = sqrt(x-4) , (ii) (|x-2|)/(x-1) = 1/(x-1)

Prove that: x^4=4=(x+1+i)(x+1-i)(x-1+i(x-1-i)dot)

If x+i y=(a+i b)/(a-i b) prove that x^2+y^2=1

If 2x - (1)/(2x) =4 , find : (i) 4x^(2) + (1)/( 4x^2)

If x + i y =(a+i b)/(a-i b), prove that x^2+y^2=1 .

Solve each of the following equation for real x and y : (x+ yi) + (3-2i) =1 + 4i

If x+1/x=6 , find (i) x^2+1/(x^2) (ii) x^4+1/(x^4)

Find x and y if (x^4+2x i)-(3x^2+y i)=(3-5i)+(1+2y i)

If the normal at four points P_(i)(x_(i), (y_(i)) l, I = 1, 2, 3, 4 on the rectangular hyperbola xy = c^(2) meet at the point Q(h, k), prove that x_(1) + x_(2) + x_(3) + x_(4) = h, y_(1) + y_(2) + y_(3) + y_(4) = k x_(1)x_(2)x_(3)x_(4) =y_(1)y_(2)y_(3)y_(4) =-c^(4)