The sum of two complex numbers a+ib and c+id is purely imaginary if

The modulus of the complex number z =a +ib is

The complex number z is purely imaginary , if

The conjugate of the complex number (a+ib) is :

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

The sum and product of two complex numbers are real if and only if they are conjugate of each other.

If complex number (3+2i sin x)/(1-2i sin x) is purely imaginary then x= npi+-pi/6 b. n p+-pi/3 c. 2npi+-pi/3 d. 2npi+-pi/6

lf z(!=-1) is a complex number such that [z-1]/[z+1] is purely imaginary, then |z| is equal to

The number of distinct complex number(s) z, such that |z|=1 and z^(3) is purely imagninary, is/are equal to

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 equaiton az^(2) + bz + c=0 , where a,b,c are complex number. If equaiton has two purely imaginary roots, then which of the following is not ture.