MAT1005 Exam 4 Name ________________________________________

1. Use the initiator and generator below to generate the next two stages of the iterated fractal.

2. Use the initiator and generator below to generate the next two stages of the iterated fractal.

3. Determine the dimension of your fractal generated in problem 2.

4. Plot each number in the complex plane. a) 2 b) 2i c) -2 + 2i d) 2 – 2i

5. Compute (3+i) + 3(2 + 2i) + 4i(2i).

6. Use the Caesar cipher with a shift of 2 to encrypt the message “I love math”

7. Compute 25 mod 3.

8. Use the substitutional mapping below to encrypt the message “December 25, 2018”

Original: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z o 1 2 3 4 5 6 7 8 9

Maps to: 2 B Q F 5 W R T D8 I J 6 H L C O S U V K3 A 0 X 9 Y Z N 1 G 4 ME7 P

9. Use the substitution mapping in problem 8 to decrypt the message 52UV5S.

10. Encrypt the message “Liberal Arts Math” using a transposition cipher with rows 6 characters long.

11. Simplify

12. Multiply 4 – i and 2 + 2i.

13. Determine if c = -1 – i is in the Mandelbrot set.

14. Compute 113 mod 3.

15. Determine the dimension given the initiator and generator below.

MAT1005 E4FA