If `z=|(1+i, 5+2i, 3-2i),(7i, -3i, 5i),(1-i, 5-2i, 3+2i)|` then (A) z is purel imaginary (B) z is purely real (C) z has equal real and imaginary parts (D) z has positive real and imaginary parts.

Write the real and imaginary parts of the complex number: - (1/5+i)/i

Write the real and imaginary parts of the complex number: sqrt(5)/7 i

Write the real and imaginary parts of the complex number: 2-i sqrt(2)

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

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

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

If |z_1|=|z_2| and arg((z_1)/(z_2))=pi , then z_1+z_2 is equal to (a) 0 (b) purely imaginary (c) purely real (d) none of these

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

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