[" 2."vec " 6"" Prove in "vec b" That "],[qquad (1+iy)^(1/2)+(1-iy)^(1/2)=sqrt(2(x+4))]

If y= sqrt(x^2+6x+8) , then show that (1+ iy)^(1//2)+(1-iy)^(1//2)= sqrt(2(x+4)) .

If (x+iy)(1+i)=2 then

For anyy two vectors vec(a) and vec(b) , show that (1+|vec(a)|^(2))(1+|vec(b)|^(2))= |(1-vec(a).vec(b))|^(2)+|vec(a)+vec(b)+(vec(a)xx vec(b))|^(2)

If vec(a)_(1) and vec(a)_(2) are two collinear unit vectors and if |vec(a)_(1)+vec(a)_(2)|=sqrt(3) , then the value of (vec(a)_(1)-vec(a)_(2)).(2vec(a)_(1)+vec(a)_(2)) is

If vec a and vec b are non-collinear vectors,then the value of x for which vectors rarrvec alpha=(x-2)vec a+vec b and vec beta=(3+2x)vec a-2vec b are collinear,is given by (i) (1)/(2)(iii)(1)/(4)(iii)0(iv)-1

If y=sqrt(x^2+6x+8) then show that one of the value of sqrt(1+iy)+sqrt(1-iy) is sqrt(2x+8) (i=sqrt(-1))

If z=x+iy and |2z-1|=|z-2|," prove that" " " x^(2)+y^(2)=1.

If vec a,vec b,vec c be three vectors such that |vec a+vec b+vec c|=1,vec c=lambda(vec a xxvec b) and |vec a|=(1)/(sqrt(2)),|vec b|=(1)/(sqrt(3)),|vec c|=(1)/(sqrt(6)), then the angle between vec a and vec b is

Prove that log ((sin(x+iy))/(sin(x-iy))) = 2i tan^-1 ( cot x tan hy).