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Complex & Imaginary Numbers

Learn about imaginary unit, square root of negative numbers, complex numbers, and operations involving the imaginary unit i. Dive into powers of i, examples, and arithmetic with complex numbers in this introductory guide.

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Complex & Imaginary Numbers

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  1. Complex & Imaginary Numbers

  2. 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.

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

  4. Powers of i ¡= 2 ¡ = 3 ¡ = 4 ¡ =

  5. Examples

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

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

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

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