If `a=(1+i)/sqrt2," where "i=sqrt(-1),` then find the value of `a^(1929)`.

If |z-2i|lesqrt(2), where i=sqrt(-1), then the maximum value of |3-i(z-1)|, is

If x=-1-i sqrt(3) then the value of x^(3) is

If sin A = sqrt(3)/2 find the value of 2 cot^(2) A-1 .

If alpha and beta are the complex roots of the equation (1+i)x^(2)+(1-i)x-2i=o where i=sqrt(-1) , the value of |alpha-beta|^(2) is

If z=(-2)/(1+sqrt(3) i) , then the value of arg z is

Express (1+i)^(-1) ,where, i= sqrt(-1) in the form A+iB.

If 2x=-1+sqrt(3)i , then the value of (1-x^(2)+x)^(6)-(1-x+x^(2))^(6)=

If z=(sqrt(3)-i)/2 , where i=sqrt(-1) , then (i^(101)+z^(101))^(103) equals to

Find the principal value of "cosec"^-1(-sqrt2) .

If the multicative inverse of a comlex number is (sqrt3+4i)/19, where i=sqrt-1, find the complex number.