Question

complex numbers online practice
complete this assessment to review what youve learned. it will not count toward your grade.
which of the following re - expresses $5 - 2sqrt{-18}$ as a complex number in the standard form $a + bi$? (1 point)
$\bigcirc\\ 5 - 6sqrt{2}$
$\bigcirc\\ 5 - 6isqrt{2}$
$\bigcirc\\ 5 - 3sqrt{2}i$
$\bigcirc\\ 5 - 3isqrt{2}$

Explanation:

Step1: Recall \( \sqrt{-n} = i\sqrt{n} \)

We know that for a negative number under the square root, \( \sqrt{-18} = \sqrt{18 \times (-1)} = \sqrt{18} \times \sqrt{-1} = i\sqrt{18} \) (since \( \sqrt{-1}=i \)).

Step2: Simplify \( \sqrt{18} \)

Simplify \( \sqrt{18} \): \( \sqrt{18} = \sqrt{9\times2} = \sqrt{9}\times\sqrt{2} = 3\sqrt{2} \). So \( \sqrt{-18} = i\times3\sqrt{2}=3i\sqrt{2} \).

Step3: Substitute back into the expression

The original expression is \( 5 - 2\sqrt{-18} \). Substitute \( \sqrt{-18} = 3i\sqrt{2} \) into it:
\( 5 - 2\times(3i\sqrt{2}) = 5 - 6i\sqrt{2} \)

Answer:

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