If the complex numbers is `(1+ri)^(3)=lambda(1+i)`, when `i=sqrt(-1)`, for some real `lambda`, the value of r can be

If z=lambda+3+i sqrt(3-lambda^(2)), for all real lambda, then the locus of z is

If the conjugate of a complex numbers is 1/(i-1) , where i=sqrt(-1) . Then, the complex number is

If the conjugate of a complex numbers is 1/(i-1) , where i=sqrt(-1) . Then, the complex number is

If the conjugate of a complex numbers is 1/(i-1) , where i=sqrt(-1) . Then, the complex number is

If the conjugate of a complex numbers is 1/(i-1) , where i=sqrt(-1) . Then, the complex number is

Polar form of the complex number (sqrt(3)+i)/(1-i) is

Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1 ) Prove that each of these complex numbers is the square of the other

If the expression (2-i)/(2 +i) is written as the complex number a + bi, where a and b are real numbers, then what is the value of a ? (Note: i = sqrt-1)

Represent the complex numbers -1+i and (-sqrt(3)-i) in polar form.

If the expression (1 + ir)^3 is of the form of s(1+ i) for some real 's' where 'r' is also real and i = sqrt(-1) then the value of r can be