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

(frac{1+i}{1-i})^2 =?

( i^57 + frac{1}{i^25} ) =

If (frac{1+i}{1-i})^x = 1, then

i^65+frac{1}{i^145} =

Evaluate: ( i^31 + frac{1}{i^67} )

Prove the following: 2tan^-1(frac{1}{3}) = tan^-1(frac{3}{4})

prove that tan^-1(sqrtx) = frac{1}{2}cos^-1(frac{1-x}{1+x}) , if x in [0,1]

If the curvs a x^2 + b y^2 = 1 and a' x^2 + b' y^2 =1 intersect orthogonally, then prove that frac{1}{a} - frac{1}{b} = frac{1}{a'} - frac{1}{b'}

Prove the following: 2tan^-1(frac{1}{3}) + tan^-1(frac{1}{7}) = frac{pi}{4}

Simplify: i^68 + frac{1}{i^145}