Question

solve the equation using the method of your choice.
\\( y^2 - 6y + 13 = 0 \\)

the solution set is
(type an exact answer, using radicals as needed. express complex numbers in terms of \\( i \\). use a comma to separate answers as needed.)

Explanation:

Step1: Identify quadratic coefficients

For $y^2 - 6y + 13 = 0$, $a=1$, $b=-6$, $c=13$

Step2: Apply quadratic formula

Quadratic formula: $y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$y=\frac{-(-6)\pm\sqrt{(-6)^2-4(1)(13)}}{2(1)}$

Step3: Calculate discriminant

Compute discriminant:
$\sqrt{36-52}=\sqrt{-16}=4i$

Step4: Simplify the expression

Substitute back and simplify:
$y=\frac{6\pm4i}{2}=3\pm2i$

Answer:

$\{3+2i, 3-2i\}$