If `z= ((sqrt3)/(2) + (i)/(2))+ ((sqrt3)/(2)- (i)/(2))`, then prove that Im(z)= 0.

If z (2- 2 sqrt3i)^(2)= i(sqrt3+i)^(4) , then arg(z)=

If x=(1+i)/sqrt2 , prove that x^2 = i

(sqrt3+sqrt2)^(4)- (sqrt3-sqrt2)^(4) =

If z = ((sqrt3 + i) ^(3) ( 3i + 4) ^(2))/( ( 8 + 6 i ) ^(2)), then |z| is equal to

If z=(-1)/(2)+i(sqrt(3))/(2) , then 8+10z+7z^(2) is equal to a) -(1)/(2)-i(sqrt(3))/(2) b) (1)/(2)+isqrt(3)/(2) c) -(1)/(2)+i(3sqrt(3))/(2) d) (sqrt(3))/(2)i

If z _(r) = cos ((pi)/(2 ^(r))) + i sin ((pi )/( 2 ^(r))), then z _(1) . z _(2). z _(3)... upto oo equals : a)-3 b)-2 c)-1 d)0

The value of "sin"(31)/(3)pi is a) (sqrt3)/(2) b) (1)/(sqrt2) c) (-sqrt3)/(2) d) (-1)/(sqrt2)

Express (-sqrt(3)+sqrt(-2))(2 sqrt(3)-i) in the form of a+i b

If z= cos (pi)/(3) - i sin (pi)/(3) then z^(2)-z+1 is equal to