Solve sqrt{-1/2}

$$\sqrt { - \frac { 1 } { 2 } }$$

Evaluate (complex solution)

$$\frac{\sqrt{2}i}{2}\approx 0.707106781i$$

Solution Steps

Rewrite the square root of the division \sqrt{-\frac{1}{2}} as the division of square roots \frac{\sqrt{-1}}{\sqrt{2}}.

$$\frac{\sqrt{-1}}{\sqrt{2}}$$

Calculate the square root of -1 and get i.

$$\frac{i}{\sqrt{2}}$$

Rationalize the denominator of \frac{i}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{i\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{i\sqrt{2}}{2}$$

Divide i\sqrt{2} by 2 to get \frac{1}{2}i\sqrt{2}.

$$\frac{1}{2}i\sqrt{2}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$