Factor x^2+1

Problem

x2+1

Solution

1. Identify the expression as a sum of squares, which does not have a factorization over the set of real numbers.

2. Apply the complex number identity a2+b2=(a+b*i)*(a−b*i) to factor the expression over the complex numbers.

3. Substitute a=x and b=1 into the identity.

4. Write the final factored form using the imaginary unit i where i2=−1

Final Answer

x2+1=(x+i)*(x−i)

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