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

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

Find the real values of theta when (3+2 i sin theta)/(1-2i sin theta) will be purely imaginary.

If a ,b ,c are nonzero real numbers and a z^2+b z+c+i=0 has purely imaginary roots, then prove that a=b^2c dot

Prove that z=i^i, where i=sqrt-1, is purely 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.

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

If z=(3+7i)(a+ib) , where a , b in Z-{0} , is purely imaginery, then minimum value of |z| is

If Z=|{:(1,1+2i , 5i),(1-2i, -3, 5+3i),(5i, 5-3i, 7):}| , then (i =sqrt(-1))

If z=x+iyand(z-i)/(z+1) is purely imaginary, then show that the point z always lies on a circle.

If z=x+iy and (z-i)/(z+1) is purely imaginary,then show that the point z always lies on a circle.