Question

If z be a complex number satisfying z ki power 4 + z cube + to z square + z + 1 equal to zero then find the value of mod z bar

Answer 1

$\mathfrak{The\:Answer\:is}$


If z=a+ib,

z^4=(a^4+4a^3.(ib)+6a^2(ib)^2+4a.(ib)^3+(ib)^4)

z^3=(a^3+3a^2.(ib)+3a.(ib)^2+(ib)^3)

z^2=(a^2+2a.(ib)+(ib)^2

i=√-1, i^2=-1, i^3=-i, i^4=1,

F(z)= x + iy, and |F(z)|=(x^2+y^2) and angle ©=tan^-1(y/x). adding all the above. The numerical values of the complex and imaginary part is assumed to be x and y, and x^/2+y^2/2=0, gives the paraboloid and it's solution sine x is F'(z), and the modulus is the sum of the series of sine between 0 and 1, using Leibnitz sine series expansion.

This generally is the philosophy.



$\boxed{Hope\:This\:Helps}$