Evaluate (-8+ square root of -12)/40

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$\frac{- 8 + \sqrt{- 12}}{40}$

Pull out imaginary unit $i$ .

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Rewrite $- 12$ as $- 1 (12)$ .

$\frac{- 8 + \sqrt{- 1 (12)}}{40}$

Rewrite $\sqrt{- 1 (12)}$ as $\sqrt{- 1} \cdot \sqrt{12}$ .

$\frac{- 8 + \sqrt{- 1} \cdot \sqrt{12}}{40}$

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{- 8 + i \cdot \sqrt{12}}{40}$

Simplify the numerator.

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Rewrite $12$ as $2^{2} \cdot 3$ .

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Factor $4$ out of $12$ .

$\frac{- 8 + i \cdot \sqrt{4 (3)}}{40}$

Rewrite $4$ as $2^{2}$ .

$\frac{- 8 + i \cdot \sqrt{2^{2} \cdot 3}}{40}$

Pull terms out from under the radical.

$\frac{- 8 + i \cdot (2 \sqrt{3})}{40}$

Move $2$ to the left of $i$ .

$\frac{- 8 + 2 i \sqrt{3}}{40}$

Simplify terms.

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Cancel the common factor of $- 8 + 2 i \sqrt{3}$ and $40$ .

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Factor $2$ out of $- 8$ .

$\frac{2 \cdot - 4 + 2 i \sqrt{3}}{40}$

Factor $2$ out of $2 i \sqrt{3}$ .

$\frac{2 \cdot - 4 + 2 (i \sqrt{3})}{40}$

Factor $2$ out of $2 \cdot - 4 + 2 (i \sqrt{3})$ .

$\frac{2 \cdot (- 4 + i \sqrt{3})}{40}$

Cancel the common factors.

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Factor $2$ out of $40$ .

$\frac{2 \cdot (- 4 + i \sqrt{3})}{2 (20)}$

Cancel the common factor.

$\frac{2 \cdot (- 4 + i \sqrt{3})}{2 \cdot 20}$

Rewrite the expression.

$\frac{- 4 + i \sqrt{3}}{20}$

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- 1 (4) + i \sqrt{3}}{20}$

Factor $- 1$ out of $i \sqrt{3}$ .

$\frac{- 1 (4) - (- i \sqrt{3})}{20}$

Factor $- 1$ out of $- 1 (4) - (- i \sqrt{3})$ .

$\frac{- 1 (4 - i \sqrt{3})}{20}$

Move the negative in front of the fraction.

$- \frac{4 - i \sqrt{3}}{20}$

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Name

Name	one billion three hundred eighty-six million nine hundred sixty-two thousand six hundred sixty-three

Interesting facts

1386962663 has 8 divisors, whose sum is 1469158560
The reverse of 1386962663 is 3662696831
Previous prime number is 2609

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 50
Digital Root 5

Name

Name	one billion six hundred sixty-one million three hundred eighty-three thousand two hundred twelve

Interesting facts

1661383212 has 32 divisors, whose sum is 4996976400
The reverse of 1661383212 is 2123831661
Previous prime number is 389

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 33
Digital Root 6

Name

Name	two hundred eighty-three million one hundred five thousand three hundred thirty-six

Interesting facts

283105336 has 16 divisors, whose sum is 955480536
The reverse of 283105336 is 633501382
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 31
Digital Root 4

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