If `z=|[-5, 3+4i,5-7i],[3-4i,6 ,8+7i],[5+7i,8-7i,9]|,t h e nz` is (a) purely real (b)purely imaginary (c)an imaginary number that is not purely imaginary,a+i b ,`w h e r ea!=0,b!=0` (d)both purely real and purely imaginary

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

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

Which term of the sequence 12+8i ,\ 11+6i ,\ 10+4i ,... is (a) purely real and (b). purely imaginary?

Prove that z=i^i ,w h e r ei=sqrt(-1) , is purely real.

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

Which term of the sequence 8-6i ,7-4i ,6-2i ,..... is (i) purely real (ii) 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

Let z!=i be any complex number such that (z-i)/(z+i) is a purely imaginary number. Then z+ 1/z is

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