Question

write the number as the product of a real number and ( i ).
( sqrt{-20} )
( sqrt{-20} = square )
(simplify your answer. type your answer in the form ( a + bi ). type an exact answer, using radicals as needed.)

Explanation:

Step1: Separate negative from radical

$\sqrt{-20} = \sqrt{20 \times (-1)}$

Step2: Apply imaginary unit definition

$\sqrt{20 \times (-1)} = \sqrt{20} \times \sqrt{-1} = \sqrt{20}i$

Step3: Simplify the radical

$\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$

Step4: Combine terms

$2\sqrt{5}i = 0 + 2\sqrt{5}i$

Answer:

$0 + 2\sqrt{5}i$ (or $2\sqrt{5}i$)