Values `(s)(-i)^(1//3)` is/are `(sqrt(3)-i)/2` b. `(sqrt(3)+i)/2` c. `(-sqrt(3)-i)/2` d. `(-sqrt(3)+i)/2`

If z is a complex number such that |z|=4 and a r g(z)=(5pi)/6 , then z is equal to -2sqrt(3)+2i b. 2sqrt(3)+i c. 2sqrt(3)-2i d. -sqrt(3)+i

If z is a complex number such that |z|=4 and a r g(z)=(5pi)/6 , then z is equal to -2sqrt(3)+2i b. 2sqrt(3)+i c. 2sqrt(3)-2i d. -sqrt(3)+i

show that ((sqrt(3)+i)/2)^6+((i-sqrt(3))/2)^6=-2

Prove that ((i-sqrt(3))/(i+sqrt(3)))^(100)+((i+sqrt(3))/(i-sqrt(3)))^(100)=-1

The complex number, z=((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(3)i))

Find the value of a and b if (i)(sqrt(3)+1)/(sqrt(3)-1)=a+bsqrt(3)" "(ii)(5+2sqrt(3))/(5-2sqrt(3))=a+bsqrt(3)

Simplify: (i) (5+\ sqrt(5))\ (5-\ sqrt(5)) (ii) (3+2sqrt(2))\ (3-2sqrt(2))

If 3^(49)(x+i y)=(3/2+(sqrt(3))/2i)^(100) and x=k y then k is: a. -1//3 b. sqrt(3) c. -sqrt(3) d. -1/(sqrt(3))

If z is a complex number having least absolute value and |z-2+2i|=1 ,then z= (2-1//sqrt(2))(1-i) b. (2-1//sqrt(2))(1+i) c. (2+1//sqrt(2))(1-i)"" d. (2+1//sqrt(2))(1+i)

For the principal values, evaluate each of the following : (i) sin^(-1)(-1/2)+2cos^(-1)(-(sqrt(3))/2) (ii) sin^(-1)(-(sqrt(3))/2)+cos^(-1)((sqrt(3))/2)