Question

simplify the expression to $a + bi$ form: $sqrt{81} - sqrt{-128} + sqrt{100} + sqrt{-8}$

Explanation:

Step1: Simplify real square roots

$\sqrt{81}=9$, $\sqrt{100}=10$

Step2: Simplify imaginary square roots

$\sqrt{-128}=\sqrt{64\times2\times(-1)}=8\sqrt{2}i$, $\sqrt{-8}=\sqrt{4\times2\times(-1)}=2\sqrt{2}i$

Step3: Substitute back and combine reals

$9 + 10 = 19$

Step4: Combine imaginary terms

$-8\sqrt{2}i + 2\sqrt{2}i = -6\sqrt{2}i$

Step5: Combine real and imaginary parts

$19 - 6\sqrt{2}i$

Answer:

$19 - 6\sqrt{2}i$