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Complex Numbers

Complex Numbers. Lesson 1.3 day1 Notes. Complex Numbers. Learning Target: Students will be able to… Identify imaginary numbers and their place in the number system Rewrite negative radicals as complex numbers Simplify products and quotients involving radicals of negative numbers.

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Complex Numbers

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  1. Complex Numbers Lesson 1.3 day1 Notes

  2. Complex Numbers • Learning Target: Students will be able to… • Identify imaginary numbers and their place in the number system • Rewrite negative radicals as complex numbers • Simplify products and quotients involving radicals of negative numbers

  3. It's any number you can imagine The Imaginary Number i • By definition • Consider powers if i

  4. Using i • Now we can handle quantities that occasionally show up in mathematical solutions • What about

  5. Imaginary part Real part Complex Numbers • Combine real numbers with imaginary numbers • a + bi • Examples

  6. The set of Complex Numbers

  7. VENN DIAGRAMRepresentation • Since all number belong to the Complex number field, C, all number can be classified as complex. The Real number field, R, and the imaginary numbers, i, are subsets of this field as illustrated below. Complex Numbers a + bi Real Numbers a + 0i Imaginary Numbers 0 + bi

  8. Try It Out • Write these complex numbers in standard form a + bi

  9. Complex Numbers on the Calculator • Possible result • Reset modeComplex formatto Rectangular • Now calculator does desired result

  10. Complex Numbers on the Calculator • Operations with complex on calculator Make sure to use the correct character for i. Use 2nd-i

  11. Warning • Consider • It is tempting to combine them • The multiplicative property of radicals only works for positive values under the radical sign • Instead use imaginary numbers

  12. Try It Out • Use the correct principles to simplify the following:

  13. Assignment • HW 1.3 #1-5, 11-28 (all), 30-46 (even)

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