question 2

Question

1. Given:

 

 

1.1. Find Z

1.2. Convert Z into polar form. Show all steps. θmust be positive

1.3. Represent Z and ALL calculated values in 1.2 on the Argand diagram

 

2. Solve for x if:

 

3. Solve for x if:

 

 

4. Given:

 

Z = (2.4 |86.3° )

Use de movire’s theorem to calculate for Z. Leave the answer in a+jb form.

 

5. Given:

 

Z= -3 -j3

 

5.1. Find Z

5.2. Convert Z in polar form. θ must be positive. Show all steps

 

6. Solve for x if:

 

7. Make y the subject of the formula if:

 

8. Determine the length and breadth of a rectangle if the length of a rectangle is 3m more than its breadth and the area of a rectangle is 54m².

 

9. Given:

 

A + 4b + 8c =0

2a - 5b = -2 + 6c

B - 4c = -3

 

Solve for c by the use of cramer’s rule

10. Make P the subject of the formlua:

 

 

11. The hypotenuse of a right angles triangle is 10mm longer than the longest of the two sides. Calculate the lengths of the sides if the shortest side is 50mm long.

 

12. Solve for x if:

 

13. Given:

 

| 1        2         3|

| 4        -1         -2|

| -3       -4         -5|

 

13.1. Calculate the value of the detrminant

13.2. What is the minor of -5

13.3. What is the co-factor of -2

 

14. Solve for x by using the determinant if:

 

x + y = 10

X - y = 2

 

15. Given:

 

2x -- 2y - Z =  3

4x + 5y - 2Z = -3

3x + 4y - 3Z = -7

 

15.1. Solve for the value of Z by using Cramer’s Rule.

15.2. Determine the value of the cofactor of -3.

 

16. Given:

 

 

Make y the subject of the formula.

 

17. Solve for x:

18. The sum of two numbers is 10. The difference of their squares is 50. Calculate the two numbers.

 

19. Solve for x and  if:

 

20. Given:

 

 

Convert z into polar form. Show ALL steps. θ may only be positive.

 

21. Given:

 

Z = 15.9 |49,7°

 

Express z in a+jb form. Show all steps.

 

22. Given:

 

2x + 3y - z = 4

3x + y + 2x = 13

X + 2y - 5x = -11

 

Solve for the value of x with the aid of Cramer’s Rule.

 

23. Given:

 

 

Determine the value of x and y.

 

24. Given:

 

 and

 

24.1. Determine the polar for of  and

24.2. Evaluate:

25. Simplify:

 

Answer 1

21)

Step 1:

The polar form is

Conversion from Polar to rectangular form :

and .

Substitute in the rectangular equation.

The rectangular form is 

Step 2:

De Moivres Theorem:

If is a complex number, then

where is a positive integer.

De Moivres theorem: .

Then,

Solution:

Answer 2

22)

Step 1:

 The system of equations are

Convert the equations into matrices form ,

Where is coefficient matrix, is variable matrix and is constant matrix.

Solve the equations by using Cramer's Rule.

Since Cramer's Rule is applicable.

Solution:

The value of