Imaginary and Complex Numbers - New Paltz Middle School



Imaginary and Complex Numbers Name:

Review Packet

|1. Simplify [pic] |2. Given [pic], evaluate f(i). |

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|3 Simplify [pic] |4 Simplify [pic] |

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|5 Express in simplest [pic] form: [pic] |6 Simplify [pic] |

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|7 What is [pic] subtracted from [pic]? |8 Simplify [pic]. |

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|9 Simplify [pic] |10 Simplify [pic]. |

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|11 Simplify: [pic] |12 Simplify: [pic] |

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|13 Find the roots of the function [pic] | |

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14. Given the function [pic], find the largest integral value for B that would give the function imaginary roots.

15. Given the equation [pic], find all the values of c that would give the equation real, rational, and equal roots.

16. Describe the nature of the roots of the following:

a) [pic] b) [pic]

16 cont. Describe the nature of the roots of the following:

c) [pic] d) [pic]

17. Given the sum of the roots and the product of the roots, write a quadratic equation. Write each quadratic in the form [pic] where a, b, and c are integers.

a) sum = -8 product = 10

b) sum = [pic] product = [pic]

18. Write an equation whose roots are [pic] and whose coefficients are integers.

19. Write an equation whose roots are [pic].

20. Given that a quadratic equation has root [pic], find the other root and then find a possible equation.

21. Given that the quadratic equation [pic] has root -4, find the other root of the quadratic.

22. Draw and label each complex number as a vector on the Argand Plane given.

[pic]

[pic]

[pic]

[pic]

25. Evaluate [pic]

24. Display the following sums on the Argand Planes below and state the answers.

[pic] [pic]

How would you subtract these complex numbers graphically?

[pic]

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