If `x=a+b i` is a complex number such that `x^2=3+4i and x^3=2+11i ,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 the complex numbers sinx + i cos2x and cosx- i sin2x are conjugate to each other, then x is equal to

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

If k in R_o t h e n det{a d j(k I_n)} is equal to

Let omega be the complex number cos (2 pi)/(3)+i sin (2 pi)/(3) . Then the number of distinct complex number z satisfying [[z+1,omega,omega^(2)],[omega,z+omega^2,1],[omega^(2),1,z+omega]] = 0 is equal to

If 3+i x^(2) y and x^(2)+y+4 i are conjugate complex numbers then x^(2)+y=

Find real value of x and y for which the complex numbers -3+i x^2y and x^2+y+4i are conjugate of each other.

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

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