Question

which of the following re - expresses 5 - 2\sqrt{-18} as a complex number in the standard form a + bi? (1 point)
o 5 - 6\sqrt{2}
o 5 - 3i\sqrt{2}
o 5 - 6i\sqrt{2}
o 5 - 3\sqrt{2}i

Explanation:

Step1: Simplify the square - root of negative number

Recall that $\sqrt{-x}=\sqrt{x}\cdot i$ for $x>0$. So, $\sqrt{-18}=\sqrt{18}\cdot i$. Since $18 = 9\times2$, then $\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}$. So, $\sqrt{-18}=3\sqrt{2}i$.

Step2: Multiply by the coefficient

We have $2\sqrt{-18}=2\times3\sqrt{2}i = 6\sqrt{2}i$.

Step3: Write in standard form

The original expression $5 - 2\sqrt{-18}$ becomes $5-6\sqrt{2}i$.

Answer:

$5 - 6i\sqrt{2}$ (the third option)