Math Help:Imaginary Numbers and Operations. 10 Questions. Please answer ASAP?

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

1.

x^2 = 20 = 4 X 5

x = squt (4) X squt (5) = 2 X squt (5)

2. (From the kind of problems ur assigned it seems like u got the value wrong for this problem).  Anyway, here is the solution,

x^2 +3x = 12

x^2 + 3x -12 = 0

Comparing to Ax^2 + Bx + C = 0

A = 1

B = 3

C = -12

Roots are x = (-B +- Squt[DELTA]) / 2A

where DELTA = squt (B^2 - 4AC) = squt (9 - 4*1*(-12)) = squt (57)

so x = (-3 +- Squt(57)) / 2

3.

2x^2+4x-3 = 0.

Compare with solution of problem # 2.

A = 2

B = 4

C = -3

DELTA = B^2 - 4AC = 16 + 24 = 40

x = (-4 +- squt(40)) /4

3.

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

x^2-4x+7=0

A = 1

B = -4

C = 7

DELTA = squt(16-28) = squt(-12) = squt(12 i)

(I hope you know why we put i for a negative sign)

x = (-B +- squt(DELTA)) / 2A

   = (4 +- squt(12 i)) / 2

More simplifyin,

x = ( 4 +- squt(4*3 i)) / 2

x = ( 4 +- 2 squt(3 i)) / 2

x = 2 +- squt (3i)

5.

i^5 = (i^4) * i = 1 * i = i

6.

squt(-32) = squt (- 16 X 2) = 4 squt (-2) = 4 squt(2i)

7.

similar way to # 6,

5i - 7i

8.

(-3i) (2i) = - 6 i^2 = -6

9.

(7 squt(-3)) ( 2 squt (-9*3))

(7 squt(-3)) (6 squt(-3))

=42 squt (-3)

= 42 squt (3i)

10.

squt(-24) / -2

= squt(- 6*4) / -2

= 2 squt (-6) / -2

= - squt(-6)

= - squt (6i)

HOPE THIS HELPS YOU

Answer 2

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Answer 3

Note: i = √-1

1) x² = 20

x =  +/-√20 =  Ã¢ÂˆÂš(4*5) = 2 √5 or -2√5

2) x² + 3x = 12

x² + 3x - 12 = 0

x = (-3 +/- √[3² - 4(1)(-12)])/2(1)

x = (-3 +/- √(9 + 48)]/2

x = (-3 +/- √(57)]/2

x = -3/2 + (√57)/2 or -3/2 - (√57)/2

3) 2x² + 4x -3 = 0

x = (-4 +/- √[4² - 4(2)(-3)])/2(2)

x = (-4 +/- √[16 + 24])/4

x = (-4 +/- √40)/4

x = (-4 +/- 2√10)/4

x = -1 + (√10)/2 or  -1 - (√10)/2

4) Not sure what it's supposed to be equal to. Assuming 0:

x² - 4x + 7 = 0

x = (4 +/- √[(-4)² - 4(1)(7)])/2(1)

x = (4 +/- √[16 - 28])/2

x = (4 +/- √[-12])/2

x = (4 +/- 2i√3)/2

x = 2 + i√3 or 2 - i√3

5) i^5 = (i²)*(i²)*i= (-1)(-1)i = i

6) √-32 = √(-1)(4*4*2)= 4i√2

7) √-25 - √-49 = 5i - 7i = -2i

8) -3i * 2i = -6i² = -6*-1 = 6

9) (7√-3)(2√-27) = (7i√3)(2i√27) = (7i√3)(6i√3) = 42i² * 3 = 126i² =

126 * -1 = 126

10) √-24/-2 = i√24/-2 = 2i√6/-2 = -i√6