Prove that the values of `4sqrt(-1)` are `pm (1)/(sqrt(2))(1 pm i)`.

The value of ((1+sqrt(3)i)/(1 - sqrt(3)i))^(10) is

Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di as vertices in the Argand diagram is isosceles.

Evaluate the value of tan^(-1) (-sqrt(3)) +cos^(-1) (1/(sqrt(2))) + sin^(-1) (-(sqrt(3))/2)

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

If cos^(-1)sqrt(p)+cos^(-1)sqrt(1-p)+cos^(-1)sqrt(1-q)=(3pi)/4, then the value of q is (a)1 (b) 1/(sqrt(2)) (c) 1/3 (d) 1/2

The value of lim_(x->pi/4) (sqrt(1-sqrt(sin2x)))/(pi-4x) is

The value of lim_(x->pi/4) (sqrt(1-sqrt(sin2x)))/(pi-4x) is

The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),sin^(-1)alpha are the angles of a triangle is (-1)/(sqrt(2)) (b) 1/2 (c) 1/(sqrt(3)) (d) 1/(sqrt(2))

Prove that pi/6 lt int_0^1(dx) /(sqrt(4-x^2-x^3)) lt pi/(4sqrt(2))