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=a+bi is a complex number such that x^2=3+4i and x^3=2+11i , where i=sqrt-1 , then (a+b) equal to

Prove that z=i^i ,w h e r ei=sqrt(-1) , is purely real.

If the complex numbers x and y satisfy x^3-y^3=98 ia n dx-y=7i ,t h e nx y=a+i b ,w h e r ea ,b , in Rdot The value of (a+b)//3 equals ______.

Let z_1=a+i b and z_2=c+i d are two complex number such that |z_1|=r and R e(z_1z_2)=0 . If w_1=a+i c and w_2=b+i d , then |w_2|=r (b) |w_2|=r R e(w_1w_2)=0 (d) I m(w_1w_2)=0

If A is a square matrix such that A^2=A ,t h e n(I+A)^3-7A is equal to (a) A (b) I-A (c) I (d) 3A

Evaluate the following: \ 2x^4+5x^3+7x^2-x+41 ,\ w h e n\ x=-2-sqrt(3)i

If z=(a+i b)^5+(b+i a)^5 , then prove that R e(z)=I m(z),w h e r ea ,b in Rdot

Solve the equation x^2-x+1=1/2+sqrt(x-3/4), w h e r e xgeq3/4

Let z=9+b i ,w h e r eb is nonzero real and i^2=-1. If the imaginary part of z^2a n dz^3 are equal, then b/3 is ______.

Let z=9+b i ,w h e r eb is nonzero real and i^2=-1. If the imaginary part of z^2a n dz^3 are equal, then b//3 is ______.