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

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

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

If a, b , c in R and 3b^(2)-8ac lt 0 , then the equation ax^(4)+bx^(3)+cx^(2)+5x-7=0 has a) all real roots b) all imaginary roots c)exactly two real and two imaginary roots d) none

Number of imaginary complex numbers satisfying the equation, z^2=bar(z)2^(1-|z|) is

Show x^5-2x^2+7 =0 has atleast two imaginary roots.

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 a) all real and is distinct b) all real and at least two are distinct c) at least two real d) all non-real

Consider the equation 10 z^2-3i z-k=0,w h e r ez is a following complex variable and i^2=-1. Which of the following statements ils true? (a)For real complex numbers k , both roots are purely imaginary. (b)For all complex numbers k , neither both roots is real. (c)For all purely imaginary numbers k , both roots are real and irrational. (d)For real negative numbers k , both roots are purely imaginary.

Show that the equation Z^4+2Z^3+3Z^2+4Z+5=0 has no root which is either purely real or purely imaginary.

Prove that the roots of ax^2+2bx+c=0 will be real and distinct if and only if the roots of (a+c) (ax^2+2bx+c) =2 (ac-b^2) (x^2+1) are imaginary