Write as a Function of z z^3+(1+i)z^2+(6+i)z+6=0

Problem

z3+(1+i)*z2+(6+i)*z+6=0

Solution

1. Identify the goal, which is to express the given equation as a function ƒ(z) and find its roots by factoring.

2. Group the terms of the polynomial to look for common factors.

z3+z2+i*z2+6*z+i*z+6=0

3. Rearrange the terms to group those with i and those without i

(z3+z2+6*z+6)+(i*z2+i*z)=0

4. Factor each group separately.

z2*(z+1)+6*(z+1)+i*z*(z+1)=0

5. Extract the common factor (z+1) from the entire expression.

(z+1)*(z2+i*z+6)=0

6. Define the function ƒ(z) based on the original polynomial equation.

ƒ(z)=z3+(1+i)*z2+(6+i)*z+6

Final Answer

ƒ(z)=(z+1)*(z2+i*z+6)

Want more problems? Check here!