need help with a few algebra questions?

Question

 

1. Solve 9x^2 + 16 = 0.


2. Simplify (–5 – 4i)(2 + 9i).

A. 26 – 37i
B. –46 – 53i
C. –46 – 37i
D. 26 – 53i

3. The square root of a negative number is an imaginary number.
true or false?

Answer 1

1. Solve 9x^2 + 16 = 0.

Given  9x^2 + 16 =0

9x^2 + 16 = 0

Subtract 16 from each side 

9x^2 + 16 - 16 = 0 - 16

9x^2 = -16

Divide each side by 9

9x^2 / 9 = -16 / 9

x^2 = (-1)16 / 9

x^2 = 16 i^2 / 9                                 ( i^2 = -1 )  

Take sqrt in each side

Sqrt x^2 =  Sqrt 16 i^2 / 9                   (sqrt x^2 = x ; sqrt -16 / 9 = 4i / 9 ;where i = sqrt -1 )

x = ± 4i / 3

 

Answer 2

given equation is  9x^2 + 16

subtract 16 from each side

    9x^2 + 16 -16 = -16

    9x^2 = - 16

   divide each side by  9

   9x^2 /9 = - 16 /9

  x^2 =- 16 /9

sqrt each side

sqrt x^2 = sqrt (- 16/9)

sqrt x^2 = sqrt (16i^2/9)       (  since  i^2 =-1)

      x  =4i/3

the solution is  x = 4i/3

Comments

The solution is x = ± 4i / 3.

Answer 3

2. Simplify (–5 – 4i)(2 + 9i).

Given  ( -5 - 4i ) ( 2 + 9i )

( -5 - 4i ) ( 2 + 9i ) =  -5*2 + (-5)* 9i  + ( -4i )* 2 + (-4i )*(9i)

                             = -10 + (-45i ) + ( -8i ) + ( -36 i^2)

Product of two  oposite  signs is negtive

                             = -10 -45i-8i+ ( -)36i^2                  (i^2 = -1)

                             = -10 - 53i + (-) 36*(-1)

Product of two same signs is positive

                             = -10 - 53i +36

( -5 - 4i ) ( 2 + 9i ) = 26 - 53i

Option D is correct

 

                            

 

 

Answer 4

3. The square root of a negative number is an imaginary number.
true or false?

 True

Example(1)=> sqrt (-1) = i

Example(2) => sqrt (-3) = sqrt(3) * i                ( where i = imaginary  number )

Answer 5

3) Let us assume anegtive number -9.

Squre root of -9 is √(-9)

= √(-1*9)

= √(-1) * √(9)

= i * √(9) where i² =  -1 => i = -1

= i * 3

= 3i  an imaginary number.

Therefore Squre root of a negative number is imaginary.

Therefore the statement is True.