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 z=(3+4i)^(6)+(3-4i)^(6),"where" i=sqrt(-1), then Im (z) equals to

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

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

Express the complex numbers 2-4i,-2+3i,0+5i and -2+0i in an Argand plane.

If the conjugate complex number of (x+yi)(1-2i) is 1+i then ......

Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numbers such that a+b+c = x, a + bomega + comega^2 = y, a + bomega^2 + comega = z .Then, the value of (|x|^2+|y|^2|+|z|^2)/(|a|^2+|b|^2+|c|^2)

Show that a complex number -3+2i is nearer from origin to the point 1+4i

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

If x^3-2x^2y^2+5x+y-5=0a n dy(1)=1,t h e n