Question

simplify the expression to a + bi form: $sqrt{36}-sqrt{-98}-sqrt{25}+sqrt{-128}$

Explanation:

Step1: Simplify square - roots of positive numbers

$\sqrt{36}=6$ and $\sqrt{25} = 5$.

Step2: Rewrite square - roots of negative numbers

$\sqrt{-98}=\sqrt{98}\times\sqrt{-1}=\sqrt{49\times2}\times i = 7\sqrt{2}i$ and $\sqrt{-128}=\sqrt{128}\times\sqrt{-1}=\sqrt{64\times2}\times i=8\sqrt{2}i$.

Step3: Substitute the simplified values into the original expression

$6 - 7\sqrt{2}i-5 + 8\sqrt{2}i$.

Step4: Combine like - terms

$(6 - 5)+(-7\sqrt{2}i + 8\sqrt{2}i)=1+\sqrt{2}i$.

Answer:

$1+\sqrt{2}i$