If `x=a+b i` is a complex number such that `x^2=3+4i and x^3=2+1i ,w h e r e `i= `sqrt(-1)` ` ,t h e n(a+b)` equal to ______.

If (x+iy)^(1//3)=a+ib,"where "i=sqrt(-1),then ((x)/(a)+(y)/(b)) is equal to

If the multicative inverse of a comlex number is (sqrt3+4i)\\19, where i=sqrt-1, find the complex number.

If z=ilog_(e)(2-sqrt(3)),"where"i=sqrt(-1) then the cos z is equal to

If alpha and beta are the complex roots of the equation (1+i)x^(2)+(1-i)x-2i=0 where i=sqrt(-1) , the value of |alpha-beta|^(2) is

If M is a 3xx3 matrix, where det M=1a n dM M^T=1,w h e r eI is an identity matrix, prove theat det (M-I)=0.

2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),w h e r ex in R-{-1,1}, is equal to

If z= sqrt3+i , then the argument of z^2 e^(z-i) is equal to :

The amplitude of e^(e^-(itheta)) , where theta in R and i = sqrt(-1) , is

Differentiate x^3 + sin 4x + e^(3x) w.r.t x

If (e_1, e_2, e_3) and (e'_1, e'_2, e'_3) are two sets of non-coplanar vectors such that i=1, 2, 3 we have e_i.e'_j={{:(1, if i=j), ( 0, if i!=j):} then show that [e_1 e_2 e_3][e'_1 e'_2 e'_3]=1