Question

write the number as a product of a real number and ( i ).
( sqrt{-11} )
( sqrt{-11}=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 radicand

$\sqrt{-11} = \sqrt{11 \times (-1)}$

Step2: Apply square root property

$\sqrt{11 \times (-1)} = \sqrt{11} \times \sqrt{-1}$

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

$\sqrt{11} \times i = 0 + \sqrt{11}i$

Answer:

$0 + \sqrt{11}i$ (or $\sqrt{11}i$)