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Math  /  Algebra

QuestionUse the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −62\sqrt{-62} □\square i □\square Submit

Studdy Solution

STEP 1

1. The imaginary unit ii is defined as i=−1i = \sqrt{-1}.
2. The expression −62\sqrt{-62} involves a negative number under the square root, which indicates the use of the imaginary unit.

STEP 2

1. Express −62\sqrt{-62} in terms of ii.
2. Simplify the expression to write it as a complex number.

STEP 3

Recognize that the square root of a negative number can be expressed using the imaginary unit ii. Specifically, for any negative number −a-a, −a=a⋅i\sqrt{-a} = \sqrt{a} \cdot i.
Apply this to −62\sqrt{-62}:
−62=62⋅i \sqrt{-62} = \sqrt{62} \cdot i

STEP 4

Since 62\sqrt{62} cannot be simplified further into a simpler radical form, the expression 62⋅i\sqrt{62} \cdot i is already in its simplest form.
Express the result as a complex number:
62⋅i \boxed{\sqrt{62} \cdot i}

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