Show that `(frac{1}{sqrt 2}+frac{1}{sqrt 2}i )^10`+`(frac{1}{sqrt 2}-frac{1}{sqrt 2}i )^10` = 0

Show that (frac{1+i}{sqrt 2})^8 + (frac{1-i}{sqrt 2})^8 = 2

[frac{1+i}{sqrt2}]^8+[frac{1-i}{sqrt2}]^8

(-frac{1}{2}+frac{sqrt3}{2}i)^1000 =

Show that tan^-1(frac{1}{2}) = frac{1}{3}tan^-1(frac{11}{2})

Show that tan^-1(frac{1}{2})-tan^-1(frac{1}{4}) = tan^-1(frac{2}{9})

Show that frac{9pi}{8}-frac{9}{4}sin^-1(frac{1}{3}) = frac{9}{4}sin^-1(frac{2sqrt2}{3})

Show that 2cot^-1(frac{3}{2})+sec^-1(frac{13}{12}) = frac{pi}{2}

Show that cos^-1(frac{sqrt3}{2}) + 2sin^-1(frac{sqrt3}{2}) = frac{5pi}[6}

int frac{x^2 + 3x +5}{(x+2)(x^2 + 2x +3)} dx=............ (A) log (x+2) + tan^(-1) (frac{x+1}{sqrt 2}) + c (B) log ( x+2) + logx^2 + 2x + 3 + c (C) log (x+2) -frac{1}{ sqrt 2} tan^(-1) (frac{x+1}{sqrt 2}) + c (D) log(x+2) +frac{1}{ sqrt 2 } tan^(-1) (frac{x+1}{sqrt 2}) + c

Show that frac{1-2i}{3-4i} + frac{1+2i}{3+4i} is a real