type the correct answer in each box. what values of a and b make this equation true? (4 + √(-49))…

Explanation:

Step1: Simplify square - roots

First, simplify each square - root term: $\sqrt{-49}=7i$, $\sqrt{(-4)^2} = 4$, $\sqrt{-324}=18i$. The left - hand side of the equation $(4+\sqrt{-49})-2(\sqrt{(-4)^2}+\sqrt{-324})$ becomes $(4 + 7i)-2(4 + 18i)$.

Step2: Expand the expression

Expand $-2(4 + 18i)$ using the distributive property: $-2\times4-2\times18i=-8 - 36i$. The expression is now $4 + 7i-8 - 36i$.

Step3: Combine like terms

Combine the real parts and the imaginary parts separately. Real parts: $4-8=-4$. Imaginary parts: $7i-36i=-29i$. So, $a=-4$ and $b = - 29$.

Answer:

$a=-4$ $b=-29$