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Rational vs. Irrational Numbers Identification in the Complex Number System

Learn to differentiate between rational and irrational numbers in the complex number system. Understand real and imaginary parts of complex numbers, operations with complex numbers, and use of the imaginary unit. Practice adding and multiplying complex numbers. Enhancement materials include chapter summaries, vocabulary lists, and homework assignments.

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Rational vs. Irrational Numbers Identification in the Complex Number System

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  1. Pre-calc day 4

  2. The complex number system Part ii

  3. Identify the numbers below as rational or irrational numbers Rational Rational Irrational Rational Rational

  4. Complex numbers Any number of the form a+bi, where a and b are real numbers and i is the imaginary unit is called a complex number. a is the called the real part and b is called the imaginary part. If b≠0, the number is called an imaginary number.

  5. Numbers Complex numbers a + bi Real numbers Imaginary numbers

  6. The Number System Insert at least two examples for each level.

  7. Imaginary unit The imaginary unit is i which has the following properties: Now try these

  8. Square root of negative numbers: =6i = =

  9. Example

  10. Add: (2+3i)+(4+5i) Multiply (2+3i)(4+5i)= Examples

  11. Method: rationalize the denominator Process: multiply numerator and denominator by the complex conjugate of 4+3i. Dividing; express in form of a+bi.

  12. Reminder: Reminder: write final answer in form

  13. = simplify

  14. Peruse the ch.1 summary, vocabulary list, and chapter test , starting on page 48. Homework

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