Question

evaluate ( x^2 - 4x + 2 ) for ( x = 2 + i ).( x^2 - 4x + 2 ) evaluated for ( x = 2 + i ) equals \\(\square\\).(type your answer in the form ( a + bi ).)

Explanation:

Step1: Substitute $x=2+i$

$x^2 - 4x + 2 = (2+i)^2 - 4(2+i) + 2$

Step2: Expand $(2+i)^2$

$(2+i)^2 = 2^2 + 2\cdot2\cdot i + i^2 = 4 + 4i - 1 = 3 + 4i$

Step3: Expand $-4(2+i)$

$-4(2+i) = -8 - 4i$

Step4: Combine all terms

$(3 + 4i) + (-8 - 4i) + 2 = (3-8+2) + (4i-4i)$

Step5: Simplify the expression

$3-8+2 = -3$, $4i-4i=0$

Answer:

$-3$