Solve 1/6-i/2sqrt{3}

$$\frac { 1 } { 6 } - \frac { i } { 2 \sqrt { 3 } }$$

Evaluate

$$\frac{-\sqrt{3}i+1}{6}\approx 0.166666667-0.288675135i$$

Solution Steps

Rationalize the denominator of \frac{i}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{1}{6}-\frac{i\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{1}{6}-\frac{i\sqrt{3}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{1}{6}-\frac{i\sqrt{3}}{6}$$

Divide i\sqrt{3} by 6 to get \frac{1}{6}i\sqrt{3}.

$$\frac{1}{6}-\frac{1}{6}i\sqrt{3}$$

Real Part

$$\frac{1}{6} = 0.16666666666666666$$