If `log_(sqrt3) |(|z|^2 -|z| +1|)/(|z|+2)|<2` then locus of z is

If (log)_(sqrt(3))((|z|^2-|z|+1)/(2+|z|))>2, then locate the region in the Argand plane which represents zdot

If log sqrt(3)((|z|^(2)-|z|+1)/(2+|z|))gt2 , then the locus of z is

If log_(tan30^@)[(2|z|^(2)+2|z|-3)/(|z|+1)] lt -2 then |z|=

If log_(1/2)((|z|^2+2|z|+4)/(2|z|^2+1))<0 then the region traced by z is ___

If log_(1/3) |z+1| > log_(1/3) |z-1| then prove that Re(z) < 0.

If z=i log(2-sqrt(3)) then cosz

If arg ((z_(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z_(1)|=3 , then |z_(1)| equals to a. sqrt(3) b. 2sqrt(2) c. sqrt(10) d. sqrt(26)

If z=i log(2-sqrt3), then cosz= a. -1 b. (-1)/2 c. 1 d. 2

int(dz)/(z sqrt(z^(2)-1))

If |z_(1)| = sqrt(2), |z_(2)| = sqrt(3) and |z_(1) + z_(2)| = sqrt((5-2sqrt(3))) then arg ((z_(1))/(z_(2))) (not neccessarily principal) is (a) (3pi)/(4) (b) (2pi)/(3) (c) (5pi)/(4) (d) (5pi)/(2)