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

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

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

Prove that (1+i)^4 x (1+frac{1}{i})^4 = 16

Find the value of ( i^(4x + 1 ) - i^(4x-1 ) )/2

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

If ((1+i)/(1-i))^(x)=1 , then x=

Let I be an interval disjointed from [-1,1] Prove that the function f(x)=x+(1)/(x) is increasing on I .

Prove that identity : sum_(i=1)^(n) (x_i-bar x)^2 = sum_(i=1)^(n) x_i^2-n bar x^2= sum_(i=1)^(n) x_i^2 -(sum_(i=1)^(n) x_i)^2/n .

Let I be any interval disjoint from [–1, 1]. Prove that the function f given by 1 f(x) =x+(1)/(x) is increasing on I.

Let I be any interval disjoint from [–1, 1]. Prove that the function f given by 1 f(x) =x+(1)/(x) is increasing on I.