Evaluate x^2 - 2x + 2 for x = 1 + i.

Key Concepts

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where 'a' is the real part and 'b' is the coefficient of the imaginary unit 'i', which is defined as the square root of -1. In this question, x = 1 + i is a complex number, and understanding how to manipulate complex numbers is essential for evaluating the expression.

Polynomial Evaluation

Polynomial evaluation involves substituting a given value into a polynomial expression to compute its value. In this case, the polynomial is x^2 - 2x + 2, and we need to substitute x = 1 + i into this expression. This process requires careful arithmetic, especially when dealing with complex numbers.

Imaginary Unit Properties

The imaginary unit 'i' has specific properties that are crucial for calculations involving complex numbers. Notably, i^2 = -1, which allows for simplifications when squaring complex numbers. Understanding these properties helps in correctly simplifying the terms that arise when evaluating the polynomial at complex values.