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Groups Today

Groups Today. Group 1: Myles, Kaitlyn, Victoria Group 2: Matthew, William, Emily Group 3: Darius, Vanessa Group 4: Jorge, Mariana, Anthony Group 5: Ryan, Julio, Moises Group 6: Anthony G., Le’ona, Ariadny. Complex Numbers. Imaginary Unit.

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Groups Today

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  1. Groups Today • Group 1: Myles, Kaitlyn, Victoria • Group 2: Matthew, William, Emily • Group 3: Darius, Vanessa • Group 4: Jorge, Mariana, Anthony • Group 5: Ryan, Julio, Moises • Group 6: Anthony G., Le’ona, Ariadny

  2. Complex Numbers

  3. Imaginary Unit • Until now, you have always been told that you can’t take the square root of a negative number. If you use imaginary units, you can! • The imaginary unit is ¡ • ¡= • It is used to write the square root of a negative number.

  4. Property of the square root of negative numbers • If r is a positive real number, then Examples:

  5. *For larger exponents, divide the exponent by 4, then use the remainder as your exponent instead. Example:

  6. Examples

  7. Complex Numbers • A complex number has a real part & an imaginary part. • Standard form is: Real part Imaginary part Example: 5+4i

  8. The Complex plane Real Axis Imaginary Axis

  9. Graphing in the complex plane

  10. Adding and Subtracting(add or subtract the real parts, then add or subtract the imaginary parts) Ex: Ex: Ex:

  11. MultiplyingTreat the i’s like variables, then change any that are not to the first power Ex: Ex:

  12. Partner Showdown • You will complete the problem on their own, and reveal the answer to one-another at the same time. • If your group all has the same answer, you may move on. • If you do not, you must discuss any errors and work together to clear-up any misunderstandings before moving on.

  13. Next class • You will have a quiz on this material next class. • Be sure to complete your homework!

  14. Exit Ticket

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