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Complex Numbers

Complex Numbers. 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.

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Complex Numbers

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  1. Complex 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. *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

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