Question

write the number as a product of a real number and ( i ).
( sqrt{-2} )
( sqrt{-2} = square )
(simplify your answer. type your answer in the form ( a + bi ). type an exact answer, using radicals as needed.)

Explanation:

Step1: Rewrite negative radicand

$\sqrt{-2} = \sqrt{2 \times (-1)}$

Step2: Split the square root

$\sqrt{2 \times (-1)} = \sqrt{2} \times \sqrt{-1}$

Step3: Substitute $\sqrt{-1}=i$

$\sqrt{2} \times i = \sqrt{2}i$

Step4: Match form $a+bi$

$0 + \sqrt{2}i$

Answer:

$0+\sqrt{2}i$ (or $\sqrt{2}i$)