Solve 2/1-sqrt{-3}

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

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Rationalize the denominator of \frac{2}{1-\sqrt{-3}} by multiplying numerator and denominator by 1+\sqrt{-3}.

$$\frac{2\left(1+\sqrt{-3}\right)}{\left(1-\sqrt{-3}\right)\left(1+\sqrt{-3}\right)}$$

Consider \left(1-\sqrt{-3}\right)\left(1+\sqrt{-3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Square 1. Square \sqrt{-3}.

$$\frac{2\left(1+\sqrt{-3}\right)}{1+3}$$

Subtract -3 from 1 to get 4.

$$\frac{2\left(1+\sqrt{-3}\right)}{4}$$

Divide 2\left(1+\sqrt{-3}\right) by 4 to get \frac{1}{2}\left(1+\sqrt{-3}\right).

$$\frac{1}{2}\left(1+\sqrt{-3}\right)$$

Use the distributive property to multiply \frac{1}{2} by 1+\sqrt{-3}.

$$\frac{1}{2}+\frac{1}{2}\sqrt{-3}$$