Show that `(bar(2-i))^2/(3+4i)=1.`

Show that (1- 2i )/( 3 - 4i ) + (1 + 2i )/( 3 + 4i ) is real.

Show that (1+ 2i)/(3+4i) xx (1-2i)/(3-4i) is real

Show that bar(a)=bar(i)+2bar(j)+bar(k), bar(b)=2bar(i)+bar(j)+3bar(k) and bar(c)=bar(i)+bar(k) are linearly independent.

Show that the points A(2bar(i)-bar(j)+bar(k)), B(bar(i)-3bar(j)-5bar(k)), C(3bar(i)-4bar(j)-4bar(k)) are the vertices of a right angled triangle.

If A=[(4,2),(-1,1)] , show that (A-2 I) A-3 I) =0

if z = 2 + i + 4i^(2) -6i^(3) then verify that (i) (bar(z^(2)) = (barz)^(2))

if z = 2 + i + 4i^(2) -6i^(3) then verify that (i) (bar(z^(2)) = (barz)^(2))

If bar(a)=bar(i)+2bar(j)-3bar(k),bar(b)=2bar(i)+3bar(j)+bar(k) then Show that bar(a)+bar(b),bar(a)-bar(b) are perpendicular .

Show that the points -2bar(i)+3bar(j)+6bar(k), 6bar(i)-2bar(j)+3bar(k), 3bar(i)+6bar(j)-2bar(k) form an equilateral triangle.

If z_(1)=-3+4i and z_(2)=12-5i, "show that", |(z_(1))/(z_(2))|=(|z_(1)|)/(|z_(2)|)