Given `z` is a complex number with modulus 1. Then the equation `[(1+i a)/(1-i a)]^4=z` has (a) all roots real and distinct (b)two real and two imaginary (c) three roots two imaginary (d)one root real and three imaginary

Prove that the equation Z^3+i Z-1=0 has no real roots.

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has A. only purely imaginary roots B. all real roots C. two real and purely imaginary roots D. neither real nor purely imaginary roots

The number of real root of the equation e^(x-1)+x-2=0 , is

If the equation x^4- λx^2+9=0 has four real and distinct roots, then lamda lies in the interval

If a

Consider two complex numbers alphaa n dbeta as alpha=[(a+b i)//(a-b i)]^2+[(a-b i)//(a+b i)]^2 , where a ,b , in R and beta=(z-1)//(z+1), w here |z|=1, then find the correct statement: (a)both alphaa n dbeta are purely real (b)both alphaa n dbeta are purely imaginary (c) alpha is purely real and beta is purely imaginary (d) beta is purely real and alpha is purely imaginary

If a ,b ,c are distinct positive numbers, then the nature of roots of the equation 1//(x-a)+1//(x-b)+1//(x-c)=1//x is Option a) all real and is distinct Option b) all real and at least two are distinct Option c) at least two real Option d) all non-real

If z = x + iy is a complex number such that |(z-4i)/(z+ 4i)| = 1 show that the locus of z is real axis.

The equation x-2/(x-1)=1-2/(x-1) has a. no root b. one root c. two equals roots d. Infinitely many roots