Question

Multiply:$(4-\sqrt{-12})(3-\sqrt{-48})$

Short answer

The simplified solution is$-12-22\sqrt{3}i$

Step-by-step solution

Given information

We are given an equation$(4-\sqrt{-12})(3-\sqrt{-48})$

Write the complex number as -b=bi

We get,$(4-\sqrt{12}i)(3-\sqrt{48}i)$

Use FOIL

We get, $12-4\sqrt{48}i-3\sqrt{12}i+\sqrt{576}{i}^2$

Combine like terms and simplify i2

$$\begin{gathered} 12-16\sqrt{3}i-6\sqrt{3}i-24 \\ -12-22\sqrt{3}i \end{gathered}$$

Conclusion

The solution of the above equation is$-12-22\sqrt{3}i$