Solve (sqrt{3}+sqrt{12})(1-sqrt{3}i)

$$( \sqrt { 3 } + \sqrt { 12 } ) ( 1 - \sqrt { 3 } i )$$

Evaluate

$$3\sqrt{3}-9i\approx 5.196152423-9i$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Combine \sqrt{3} and 2\sqrt{3} to get 3\sqrt{3}.

$$3\sqrt{3}\left(1-i\sqrt{3}\right)$$

Use the distributive property to multiply 3\sqrt{3} by 1-i\sqrt{3}.

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

The square of \sqrt{3} is 3.

$$3\sqrt{3}-3i\times 3$$

Multiply -3i and 3 to get -9i.

$$3\sqrt{3}-9i$$

Real Part

$$3 \sqrt{3} = 5.196152423$$