If a,b,c are comples number and z=`|{:(,0,-b,-c),(,bar(b),0,-a),(,bar(c),bar(a),0):}|` then show tha z is purely imaginary

If a, b, c are complex numbers, then the determinant Delta = |(0,-b,-c),(bar(b),0,-a),(bar(c),bar(a),0)| , is

if z-bar(z)=0 then z is purely imaginary

If |(z)/(|bar(z)|)-bar(z)|=1+|z|, then prove that z is a purely imaginary number.

If bar(z)= -z ne 0 , show that z is necessarily a purely imaginary number

([[bar(a),bar(b),bar(c)]])/([[bar(b),bar(a),bar(c)]]) =

If bar(a)+bar(b)+bar(c)=bar(0) then bar(a)timesbar(b)=

If bar(a).bar(b) = bar(a).bar(c ) and bar(a) xx bar(b) = bar(a) xx bar(c ), bar(a) != 0 , then show that bar(b) = bar(c ) .

If bar(a),bar(b),bar(c) are non-coplanar vectors such that then bar(b)xxbar(c)=bar(a),bar(c)xxbar(a)=bar(b) and bar(a)xxbar(b)=bar(c), then |bar(a)+bar(b)+bar(c)|=