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Warm-up:

Warm-up:. Perform the indicated operation. Find the area and perimeter of the box. 3. Perimeter = ____ 4. Area = ____. 2x-3. 2x+1. Complex numbers. A long long time ago, in a math class far, far away. There was no way to take the square root of a negative number.

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Warm-up:

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  1. Warm-up: Perform the indicated operation. Find the area and perimeter of the box. 3. Perimeter = ____ 4. Area = ____ 2x-3 2x+1

  2. Complex numbers

  3. A long long time ago, in a math class far, far away.. There was no way to take the square root of a negative number

  4. Every time we squared a negative number We got a positive.

  5. (-1) = 1 (-2) = 4 (-3) = 9

  6. Was there a number, that when multiplied by itself Gave you a negative???

  7. Can we in fact, take the square root of a negative number? WE CAN!!!!

  8. Ladies and Gentlemen of Geometry I present to you a NEW number... A number so complex...

  9. It stretches the imagination.. I present to you:

  10. So here’s what the math people did: They used the letter “i” to represent the square root of (-1). “i” stands for “imaginary” So, does really exist?

  11. Examples of how we use

  12. Examples of how we use

  13. i’s with exponents

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

  15. Adding and Subtracting complex numbersDo just like polynomial adding or subtracting Ex: Ex:

  16. MultiplyingDo just like polynomial multiplication but when you finish change i2 to -1 Ex: Ex:

  17. Conjugates: Two complex numbers of the form a + bi anda – bi are conjugates. The product is always a real number Ex:

  18. Dividing Complex Numbers • Multiply the numerator and denominator by the conjugate of the denominator.

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