Question

evaluate $x^2 - 6x + 7$ for $x = 3 + i$.

$x^2 - 6x + 7$ evaluated for $x = 3 + i$ equals \\(\square\\).
(type your answer in the form $a + bi$.)

Explanation:

Step1: Substitute $x=3+i$ into expression

$x^2 - 6x + 7 = (3+i)^2 - 6(3+i) + 7$

Step2: Expand $(3+i)^2$ using $(a+b)^2=a^2+2ab+b^2$

$(3+i)^2 = 3^2 + 2(3)(i) + i^2 = 9 + 6i + (-1) = 8 + 6i$

Step3: Expand $-6(3+i)$

$-6(3+i) = -18 - 6i$

Step4: Combine all terms

$(8 + 6i) + (-18 - 6i) + 7 = (8 - 18 + 7) + (6i - 6i)$

Step5: Simplify real and imaginary parts

$(8 - 18 + 7) + (6i - 6i) = -3 + 0i$

Answer:

$-3 + 0i$