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`

Which of the following is equal to root(3)(-1) a. (sqrt(3)+sqrt(-1))/2 b. (-sqrt(3)+sqrt(-1))/(sqrt(-4)) c. (sqrt(3)-sqrt(-1))/(sqrt(-4)) d. -sqrt(-1)

The incenter of the triangle with vertices (1,sqrt(3)),(0,0), and (2,0) is (a) (1,(sqrt(3))/2) (b) (2/3,1/(sqrt(3))) (c) (2/3,(sqrt(3))/2) (d) (1,1/(sqrt(3)))

The value of ((1+sqrt(3i))/(1-sqrt(3i)))^(64)+((1-sqrt(3i))/(1+sqrt(3i)))^(64) is -

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

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)

A non-zero vector vec a is such that its projections along vectors ( hat i+ hat j)/(sqrt(2)),(- hat i+ hat j)/(sqrt(2)) and hat k are equal, then unit vector along vec a is a. (sqrt(2) hat j- hat k)/(sqrt(3)) b. ( hat j-sqrt(2) hat k)/(sqrt(3)) c. (sqrt(2))/(sqrt(3)) hat j+( hat k)/(sqrt(3)) d. ( hat j- hat k)/(sqrt(2))

The values of parameter a for which the point of minimum of the function f(x)=1+a^2x-x^3 satisfies the inequality (x^2+x+2)/(x^2+5x+6)<0a r e (a) (2sqrt(3),3sqrt(3)) (b) -3sqrt(3),-2sqrt(3)) (c) (-2sqrt(3),3sqrt(3)) (d) (-2sqrt(2),2sqrt(3))

The value of ((1+sqrt3i)/(1-sqrt3i))^64+((1-sqrt3i)/(1+sqrt3i))^64

Prove that ((i-sqrt3)/(i+sqrt3))^200+((i+sqrt3)/(-i+sqrt3))^200= -1

Find the value of 4+5[-(1)/(2)-i(sqrt(3))/(2)]^(344)+3[-(1)/(2)+i(sqrt(3))/(2)]^(365) (i=sqrt(-1))