Solve (x-1-sqrt{-1})(x-1+sqrt{-1})

$$( x - 1 - \sqrt { - 1 } ) ( x - 1 + \sqrt { - 1 } )$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Apply the distributive property by multiplying each term of x-1-\sqrt{-1} by each term of x-1+\sqrt{-1}.

$$x^{2}-x+x\sqrt{-1}-x+1-\sqrt{-1}-\sqrt{-1}x+\sqrt{-1}-\left(\sqrt{-1}\right)^{2}$$

Combine -x and -x to get -2x.

$$x^{2}-2x+x\sqrt{-1}+1-\sqrt{-1}-\sqrt{-1}x+\sqrt{-1}-\left(\sqrt{-1}\right)^{2}$$

Combine x\sqrt{-1} and -\sqrt{-1}x to get 0.

$$x^{2}-2x+1-\sqrt{-1}+\sqrt{-1}-\left(\sqrt{-1}\right)^{2}$$

Combine -\sqrt{-1} and \sqrt{-1} to get 0.

$$x^{2}-2x+1-\left(\sqrt{-1}\right)^{2}$$

Calculate \sqrt{-1} to the power of 2 and get -1.

$$x^{2}-2x+1-\left(-1\right)$$

Multiply -1 and -1 to get 1.

$$x^{2}-2x+1+1$$

Add 1 and 1 to get 2.

$$x^{2}-2x+2$$