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Math  /  Algebra

QuestionUse the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −22\sqrt{-22} □\square i Submit

Studdy Solution

STEP 1

1. The imaginary unit ii is defined as i=−1i = \sqrt{-1}.
2. The expression −22\sqrt{-22} can be rewritten using the imaginary unit ii.
3. The goal is to express the radical in terms of a complex number.

STEP 2

1. Express −22\sqrt{-22} in terms of the imaginary unit ii.
2. Simplify the expression to its simplest form.

STEP 3

Recognize that −22\sqrt{-22} can be rewritten using the property of imaginary numbers:
−22=22×−1 \sqrt{-22} = \sqrt{22} \times \sqrt{-1}
Since −1=i\sqrt{-1} = i, we have:
−22=22×i \sqrt{-22} = \sqrt{22} \times i

STEP 4

Express the result as a complex number. Since 22\sqrt{22} is a real number and ii is the imaginary unit, the expression is already in the form of a complex number:
22×i=i22 \sqrt{22} \times i = i\sqrt{22}
Thus, the simplified form of the expression as a complex number is:
i22 \boxed{i\sqrt{22}}

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