A) show that z = 1 + i is a solution to the fourth degree polynomial equation z^4 − z^3 + 3z^2 − 4z + 6 = 0
b) show that z = 1 − i is a solution to the fourth degree polynomial equation z^4 − z^3 + 3z^2 − 4z + 6 = 0.

 The verification is done below.

Step-by-step explanation:  We are given to show that x = 1+i and z= 1-i are the solutions to the following fourth degree polynomial equation :

We know that

z = a is a solution of a polynomial equation f(z) if f(a) = 0.

We will be using the following value of i(iota) :

(a) Substituting z = 1+i in the left hand side of equation (i), we get

So, z = 1+i is a solution of the given polynomial equation.

(b) Similarly, substituting z = 1-i in the left hand side of equation (i), we get

So, z = 1-i is a solution of the given polynomial equation.

Hence showed.

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