Question

What values of a and b make this equation true?

Answer 1

Solution

- The best way to solve the question is to simplify the left-hand side.

- The solution steps are given below:

$\begin{gathered} (4+\sqrt{-49})-2(\sqrt{(-4^)^2}+\sqrt{(-324)})=a+bi \\ \\ (4+\sqrt{49}\times\sqrt{-1})-2(\sqrt{16}+\sqrt{324}\sqrt{-1})=a+bi \\ \\ \text{ But }\sqrt{-1}=i \\ \\ (4+7i)-2(4+18i)=a+bi \\ 4+7i-8-36i=a+bi \\ -4-29i=a+bi \end{gathered}$

Final Answer

The answer is:

$\begin{gathered} a=-4 \\ b=-29 \end{gathered}$