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

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

Evaluate (complex solution)

$$x^{2}+1$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

The square of \sqrt{-1} is -1.

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

The opposite of -1 is 1.

$$x^{2}+1$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

The opposite of -1 is 1.

$$x^{2}+1$$