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Unit 2A – Simplifying Radicals and Complex/Imaginary Numbers

Unit 2A – Simplifying Radicals and Complex/Imaginary Numbers. Honors algebra 2/Trig. Unit Goals. Students will be able to: Simplify Radicals of varying index Add, Subtract, Multiply, and Divide Radicals Rationalize the denominator when presented with radicals and radical expressions

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Unit 2A – Simplifying Radicals and Complex/Imaginary Numbers

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  1. Unit 2A – Simplifying Radicals and Complex/Imaginary Numbers Honors algebra 2/Trig

  2. Unit Goals • Students will be able to: • Simplify Radicals of varying index • Add, Subtract, Multiply, and Divide Radicals • Rationalize the denominator when presented with radicals and radical expressions • Identify and simplify complex and imaginary numbers

  3. Imaginary and Complex Numbers

  4. Warm Up/Review: • because • because • We need to introduce a new number/concept for when we have a negative number under a square root.

  5. Imaginary Numbers • An Imaginary Number exists when there is a negative under a square root • We are allowed to have negative numbers under cubed roots, for example (think about it!) • We use the letter for imaginary numbers

  6. Complex Numbers Examples: • When we combine imaginary and real numbers, we get a complex number • Example: • We can add and subtract these complex numbers like we have before! • Add the corresponding numbers and imaginary coefficients

  7. Multiplying and dividing Other Operations with Complex Numbers

  8. Multiplying Complex Numbers • We will multiply complex numbers in the same manner as when we multiplied radicals (distribution, FOIL, etc.) • It is important to remember the powers of i when we multiply. • We cannot have any powers of i in our answer other than

  9. Try on your own:

  10. Division of Complex Numbers • We CANNOT have complex numbers in the denominator. • In order to get rid of them, we can multiply both the numerator and denominator by the conjugate of the denominator.

  11. More Examples

  12. Classwork/Homework QUIZ TOMORROW Page 277-278#37, 39, 41#47-60 1st Column

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