`(1+(i)/(3))^(3)=(a+bi)/(27)` where `a,b in R` and `i=sqrt(-1)` ,then

if cos (1-i) = a+ib, where a , b in R and i = sqrt(-1) , then

Let z= a+ ib (where a,b,in R and i = sqrt(-1) such that |2z+3i| = |z^(2) identify the correct statement(s)?

What is the value of ((-1+i sqrt(3))/(2))^(3n)+((-1-i sqrt(3))/(2))^(3n), where i=sqrt(-1)?

If 8iz^(3)+12z^(2)-18z+27i=0, (where i=sqrt(-1)) then

Finid the vlues of x and y if: (i) (x+iy)(1+i)=1-i (ii) ((1+i)x-2i)/(3+i)+((2-3i)y+i)/(3-i)=i , where i=sqrt(-1) .

The value of (3sqrt(3)+(3^(5//6))i)^(3) is (where i=sqrt(-1) )

If z=(3+4i)^(6)+(3-4i)^(6),"where" i=sqrt(-1), then Im (z) equals to