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

Prove that locus of z is a circle and find its centre and radius if (z-i)/(z-1) is purely imaginary.

Find the real numbers x and y if (x-i y)(3+5i) is the conjugate of -6-24 i .

Find the real numbers x and y if (x-i y)(3+5i) is the conjugate of -6-24 i .

Find the real numbers x and y , if (x-i y)(3+5i) is the conjugate of -6-24 i

Find the real numbers x and y if (x-yi) (3+5i) is the conjugate of -6 -24i

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

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

Find the real numbers x\ a n d\ y , if (x-i y)(3+5i) is the conjugate of -6-24 idot

Find the real numbers x,y such that ( iy+ x)(3+2i) = 1+ i

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