If a+(b+2a)i=1-4i, then find a and b.

If a-5b+3ai=7-3i, then find a and b.

If a-b+2ai=3+6i, then find a and b.

If 2b+(a-b)i=2+3i, then find a and b. .

If 7a-b+5ai=7+5i, then find a and b.

If (a+b)-i(3a+2b)=5+2i , then find a a n d bdot

If (a+b)+i(a-b)=2-3i find a\ a n d\ bdot

Consider, A=[(a,2,1),(0,b,0),(0,-3,c)] , where a, b and c are the roots of the equation x^(3)-3x^(2)+2x-1=0 . If matric B is such that AB=BA, A+B-2I ne O and A^(2)-B^(2)=4I-4B , then find the value of det. (B)

If vec(a)=hat(i)+hat(j)-4hat(k) " and " vec(b)=4hat(i)-hat(j)-2hat(k) , then find (i) a unit vector in the direction of the vector (2vec(a)-vec(b)) and (ii) vector and scalar components of the vector (2vec(a)-vec(b)) along coordinate axes.

(i) If a:b:c= 2:3:4 and s=27 inches, find the area of the triangle ABC. (ii) If in a triangle ABC, a=6, b=3 and cos(A-B) =4/5 then find its area.

If sqrt(3)+i=(a+i b)(c+i d) , then find the value of tan^(-1)(b//a)+tan^(-1)(d//c)