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Exploring Complex Numbers: Imaginary Unit and Operations on the Complex Plane

Learn about the imaginary unit, properties of square roots of negative numbers, graphing in the complex plane, and operations like addition, subtraction, and multiplication of complex numbers. Understand the absolute value of complex numbers and how to find it in the complex plane.

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Exploring Complex Numbers: Imaginary Unit and Operations on the Complex Plane

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  1. 4.6Complex Numbers (p. 275)

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

  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. The Complex plane Real Axis Imaginary Axis

  8. Graphing in the complex plane

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

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

  11. Absolute Value of a Complex Number • The distance the complex number is from the origin on the complex plane. • If you have a complex number the absolute value can be found using:

  12. Examples 1. 2. Which of these 2 complex numbers is closest to the origin? -2+5i

  13. Assignment

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