Pleas give me the answers to these problems, and show your work.?

Question

Solve 2. x(squared)-5x-24=0 
Solve 3. 5x(squared)=15x 
Simplify-4 i to the 18th power 
Simplify-5. 4i (3i) 
Simplify-6. (10-7i)+6+9i 
Simplify-7. (11-81)- (2-8i) 
Simplify-8. 4x(Squared)+4=0 
Simplify-9. (1+2i)(1-2i) 
Simplfy-10. 6-i over 3-3i 
Simplify-11. (2i) (3i) (4i)

 

 

Answer 1

2.

The equation is 

Answer 2

3.

The equation is 5x²  = 15x

5x² - 15x = 15x - 15x

Answer 3

5.

( 4i )( 3i )  = 12 ( i² )

Since the value of i² = -1

12( i² ) =12( -1) = -12.

Hence the value of (4i)(3i) = -12.

Answer 4

6.

(10 - 7i) +6 +9i

= 10 + 6 +(9i - 7i)

= 16 + 2i.

Hence the value of (10-7i)+(6+9i) is  16+2i .

Answer 5

7.

(11 - 81 ) - (2 - 8i )

= 11 - 81 - 2 + 8i

= -72 + 8i

Hence the value of (11- 81) -(2 - 8i) is  -72 + 8i.

Answer 6

8.

The equation is 4x² + 4 =0

4x² = - 4

x²  = - 1

x²  = i²

x = ± i

Hence the value of x is ± i.

Answer 7

9.

(1 + 2i) (1 - 2i)

This is in the form of (a + b)(a - b) = a² - b²

 = (1)² - (2i)²

= 1 - 4(i²)    [ since i² = -1]

1-4(-1) = 1+ 4 = 5.

Hence the value of (1 + 2i) (1-2i) is 5.

Answer 8

The function is 

( i )^( 18 ) = ( i³ )^6 

Since (i³) = -i

=(-i)^ 6

According to De Moivre's Theorem

Now (- i)^ 6 can be written as 

Hence the value of (i)^ 18 = -1 .

Answer 9

10.

(6 -i ) / (3 - 3i)

The complex conjugate of 3 - 3i is 3+ 3i

Now  (6-i / 3-3i) is written as tht is multiply and divide with complex conjugate

(6 - i/3-3i)(3+ 3i/3+3i)

= (6 - i) (  3 + 3i ) / [9 - ( 3i )² ]

= (6 - i ) ( 3 + 3i ) / ( 9 + 9 )     [Since  i² = -1]

= ( 6 -i )( 3 + 3i ) / 18

= (18 + 18i -3i + 3) /18

=(18 + 15i +3) / 18

=(21 +15i ) / 18

=3(7 + 5i ) /18

=(7 + 5i ) / 6.

Hence the value of (6 - i ) / (3 - 3i)  is  (7 + 5i ) / 6.

Answer 10

11.

(2i) (3i) (4i)

= ( 6i²) ( 4i )

= (6) (-1)  (4 i)   [since i² = -1]

= - 6 (4i) 

= - 24i

Hence the value of  (2i) (3i) (4i) is  - 24i.