Attention Math Genius'.Please help solve Imaginary Numbers and Operations. Best answer=10 points?

Question

Please solve ALL answers. No links to any math websites. I VERY MUCH appreciate it. And please, no complaints on me for other people doing my work.

1. x^2=20

2.x^2+3x=12

3.2x^2+4x-3=0

4. f(x)=x^2-4x+7

5. i^5

6. √-32

7. √-25 - √-49

8. (-3i)(2i)

9. (7√-3)(2√-27)

10. √-24/-2

Answer 1

>>>> complaint for other people doing your work

Answer 2

I don't even do my own homework. Good Luck, buddy.

Answer 3

i help kidslearn,  i dotn do their entire homework- i dotn accept any hwk that  just has the answer

jim- love all those "right answers"

Answer 4

1 -- easy

2  and 3 -- quadratic

4 -- what is the question?

5 -- ans: i because i^2 = -1,  i^2 * i^2 = 1

6 -- 32 is 16 * 2, +/- 4 * i * sqrt(2)

7 -- √-25 - √-49 = 5i - 7i =  -2j

8 -- -1.5

9 -- (7√-3)(2√-27) = 14 * sqrt(-3 * - 27) = 14 * sqrt(81) = 126

10 -- easy

Answer 5

10x2=20 :P

gets confused o.O

Answer 6

Ahahaha!! Nice job, Jim!

Answer 7

I'll be happy to give you just the answers.  After all, if you don't learn how to do these problems, you're one less person I'll have to compete with for a high paying technical job.

1)

x² = 20  Take the square root of both sides

√(x²) = √(20)

x = √(20)

x =  Ã¢ÂˆÂš[2²(5)]

x =  2√(5) This is an exact solution

x ≈ 2(2.236)

x ≈ 4.472  This is an approximate solution

2)

x²+3x = 12  Subtract 12 from both sides

x²+3x-12 = 0  You now have a quadratic equation which means you can get two roots (i.e. solutions).

List all the factors of -12 that add up to 3.  The factors of -12 are: (-1,12)(-2,6)(-3,4)(-4,3)(-6,2)(-12,1).  None of these add up to 3, so this quadratic equation can't be factored nicely.  Use the quadratic formula (e.g. x = [-b±√(b²-4ac)]/2a).

x = {-3±√[3²-4(1)(-12)]}/2(1)

x = {-3±√[9-4(-12)]}/2

x = {-3±√[9-4(-12)]}/2

x = [-3±√(9+48)]/2

x = [-3±√(57)]/2 Exact solution

x ≈ (-3±7.55)/2 Approximate solution

x ≈ (-3+7.55)/2

x ≈ 4.55/2

x = 2.275  This is one root.

x ≈ (-3-7.55)/2

x ≈ (-10.55)/2

x ≈ -5.275  This is the other root

3)

2x²+4x-3=0  Again this is a quadratic equation.  There will be two roots (solutions).

Write out the factors of -3, and for each number in the set multiply by 2 and see if any add up to 4.  Take my word for it there's no such set of numbers that work.  This means you'll have to use the quadratic formula again.

x = {-b±√[b²-4(a)c]}/2a

x = {-4±√[4²-4(2)(-3)]}/2(2)

x = {-4±√[16-(-24)]}/4

x = {-4±√[16-(-24)]}/4

x = {-4±√[40]}/4 This is the exact answer.

x ≈ {-4±6.325}/4 This is an aproximate answer.

x ≈ {-4+6.325}/4

x ≈ {2.325}/4

x ≈ 0.581  This is one root.

x ≈ {-4-6.325}/4

x ≈ {-10.325}/4

x ≈ -2.581  This is the other root.

4)

f(x)=x²-4x+7

There's nothing to do with this function.  It can't be factored, or simplified, and there is no value for "x" to plug in to solve.  You're on your own with this one.

5)

i^5

remember that i= √(-1) so i² = -1 and i^4 = (i²)² = -1² = 1.

Now I^5 = i^4(i) = 1(i) = i

6)

√(-32) =

√[-1(32)] =

√(-1)√(32) =

i√(32) = Factor 32 into 2 times 16.

i√[(2)16] =

i√(2)√(16) =

4i√(2)

7)

√(-25) - √(-49) =

√[(-1)25] - √[-1(49)] =

√(-1)√(25) - √(-1)√(49) =

i√(25) - i√(49) =

i(5) - i(7) = Factor the two terms.

i(5 - 7) =

-2i

8)

(-3i)(2i) = Rearrange the expression.

-3(2)(i²) = Remember i =√(-1) so i² = -1

-6(-1) =

6

9)

[7√(-3)] [2√(-27)] = Rearrange the expression.

[7(2) √(-3) √(-27)] =

14 √(-3) √(-27) = Factor out the -1 under the radicals.

14 √[(-1)(3)] √[(-1)(27)] =

14 √(-1) √(3) √(-1) √(27) = Convert √(-1) =i

14 (i) √(3) (i) √(27) =  Gather like values.

14 (i²) √(3) √(27) = Factor 27 =into 3(3)²

14 (-1) √(3) √[3(3²)] =

-14 √(3) √(3) √(3²) =  Gather like values.

-14 [√(3)]² 3 =

-14 (3) 3 =

-14 (9) =

-126 =

10)  This problem was confusing.  I don't know if the square root applies to the numerator only, or to the whole fraction.  I'm going to make an asumption that it applies to the whole fraction.

√(-24/-2) =

√(-2(12)/-2) =  Divide out the -2/-2 = 1

√(12) = Factor 12 = 3(4) = 3(2²)

√[3(2²)] =

√(3) √(2²) =

2√(3) =

If the problem was supposed to be

√(-24)/-2 =

√[-1(2²)6]/-2 =

[√(-1) √(2²) √(6)]/-2 =

[(2) (i) √(6)]/-2 =  Remember that 2/-2 = -1

(-1) (i) √(6) =

-i√(6) =

Answer 8

32

4

15

12

-37

23

64

19

53

78