Question

What are the values of a and b if this solution is written in the form x = a + bi, where a and b are real numbers?

Answer 1

Simplifying the radical we have:

`\begin{gathered} \sqrt[]{-48}=\sqrt[]{-1}\cdot\sqrt[]{48}(\text{ Using the product rule of radicals)} \\ \sqrt[]{-1}\cdot\sqrt[]{48}=\sqrt[]{-1}\cdot\sqrt[]{2\cdot2\cdot2\cdot2\cdot3}\text{ (Using prime factorization)} \\ \sqrt[]{-1}\cdot\sqrt[]{2^4\cdot3}=(\sqrt[]{-1})(2^2\sqrt[]{3})(\text{ Simplifying)} \\ (4^{}\sqrt[]{3})i(\text{ Changing }\sqrt[]{-1}\text{ for i)} \\ \text{ We can see that the answer is a=3 and b=4}\sqrt[]{3} \end{gathered}`