If i = sqrt(-1) , then 4+5(-frac{1}{2}+f...

If `i = sqrt(-1)` , then `4+5(-frac{1}{2}+frac{isqrt3}{2})^334+3(-frac{1}{2}+frac{isqrt3}{2})^365` is equal to

A

`A.1-isqrt3`

B

`B.-1+isqrt3`

C

`C.isqrt3`

D

`D.-isqrt3`

Verified by Experts

Similar Questions

Explore conceptually related problems

If i=sqrt(-1) , then 4+5[frac{-1}{2}+frac{isqrt(3)}{2}]^334+3[frac{-1}{2}+frac{isqrt(3)}{2}]^365 =

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

[frac{sqrt3+i}{2}]^6+[frac{i-sqrt3}{2}]^6 is equal to

frac{(-1+isqrt3)^15}{(1-i)^20}+frac{(-1-isqrt3)^15}{(1+i)^20} is equal to

If omega is a complex root of the equation z^3 = 1 , then omega+(omega)^[(frac{1}{2}+ frac{3}{8}+frac{9}{32}+frac{27}{128}+…...) is equal to

If z=[frac{sqrt3}{2}+frac{i}{2}]^5+[frac{sqrt3}{2}-frac{i}{2}]^5 , then

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

Value of [frac{-1+sqrt(-3)}{2}]^40 +[frac{-1-sqrt(-3)}{2}]^40 is

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