Prove that:
`L = I omega`

Prove that: tau = I alpha

If f(x) = log_e x, x > 0 , prove that : f (uvw) = f (u) + f (v) +f (w).

If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0 , then prove that x: y : z = 1 : 1 : 1 OR 1 :omega:omega^2 OR 1:omega^2:omega , where omega is one ofthe complex cube root of unity.

Prove that: adj.I_n=I_n

For a prism prove that A + delta = i+e

Prove that t a n(i(log)_e((a-i b)/(a+i b)))=(2a b)/(a^2-b^2)(w h e r ea ,b in R^+)

If omega!=1 is a complex cube root of unity, then prove that [{:(1+2omega^(2017)+omega^(2018)," "omega^(2018),1),(1,1+2omega^(2018)+omega^(2017),omega^(2017)),(omega^(2017),omega^(2018),2+2omega^(2017)+omega^(2018)):}] is singular

Prove that [a b c][u v w]=|[a*u, b*u, c*u], [a*v, b*v, c*v], [a*w, b*w, c*w]|

Prove that : (1-i)^2= -2i .

Prove that triangle = |[a+bx,c+dx,p+qx],[ax+b,cx+d,px+q],[u,v,w]| = (1-x^2)|[a,c,p],[b,d,q],[u,v,w]|