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Math  /  Algebra

Question5+−81=5+\sqrt{-81}= (Simplify your answer, using radicals as needed. Type your an

Studdy Solution

STEP 1

1. The expression involves a real number and an imaginary number.
2. We need to simplify the expression using complex numbers.
3. The square root of a negative number involves the imaginary unit ii, where i2=−1i^2 = -1.

STEP 2

1. Simplify the square root of the negative number.
2. Combine the real and imaginary parts.

STEP 3

Simplify −81\sqrt{-81} using the imaginary unit ii.
−81=81×−1 \sqrt{-81} = \sqrt{81} \times \sqrt{-1}
Since 81=9\sqrt{81} = 9 and −1=i\sqrt{-1} = i, we have:
−81=9i \sqrt{-81} = 9i

STEP 4

Combine the real part 55 with the imaginary part 9i9i.
The expression becomes:
5+9i 5 + 9i
This is the simplified form of the expression using radicals as needed.

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