`1/(i-1) + 1/(i+1)` is a. purely imaginary b. purely rational number. c. purely integer d. negative integer

If z is a purely imaginary number then arg (z) may be

If z=1+it h e nz^(10) reduces to: A purely imaginary number An imaginary number A purely real number A complex number

The complex number z is purely imaginary , if

If (z+1)/(z+i) is a purely imaginary number (where (i=sqrt(-1) ), then z lies on a

If (z-1)/(z+1) is a purely imaginary number (z ne - 1) , then find the value of |z| .

If z is a unimodular number (!=+-i) then (z+i)/(z-i) is (A) purely real (B) purely imaginary (C) an imaginary number which is not purely imaginary (D) both purely real and purely imaginary

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: both alphaa n dbeta are purely real both alphaa n dbeta are purely imaginary alpha is purely real and beta is purely imaginary beta is purely real and alpha is purely imaginary

Find the real number x if (x−2i)(1+i) is purely imaginary.

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.

Consider a quadratic equation az^2 + bz + c =0 where a, b, c, are complex numbers. Find the condition that the equation has (i) one purely imaginary root (ii) one purely real root (iii) two purely imaginary roots (iv) two purely real roots