Write the polar form of `-(1)/(2)-(isqrt3)/2`
(Where, `i=sqrt(-1)).`

Find the all complex numbers satisying the equation 2|z|^(2)+z^(2)-5+isqrt(3)=0, wherei=sqrt(-1).

Write the following in the form a+ib (1+i)^2/(3-i)

If |z-1|=1, where z is a point on the argand plane, show that (z-2)/(z)=i tan (argz),where i=sqrt(-1).

Convert the following in the polar form : (1+7i)/(2-i)^2 .

Express the following in the polar form : (-16)/(1+ sqrt3 i) .

Write the principal value of tan^-1(sqrt3) + cosec^-1 (-2)

Write the following in the simplest form cot^(-1)((1)/(sqrt(x^(2)-1)))

The value of the determinant |{:(sqrt(6),2i,3+sqrt(6)i),(sqrt(12),sqrt(3)+sqrt(8)i,3sqrt(2)+sqrt(6)i),(sqrt(18),sqrt(2)+sqrt(12)i,sqrt(27)+2i):}| is (where i= sqrt(-1)

Express the following in polar form : - 4+4 sqrt3 i .

Express the following in the polar form : -1 -i .