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5.4 Complex Numbers

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5.4 Complex Numbers

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    1. 5.4 Complex Numbers Goals: Solve quadratic equations with complex solutions and perform operations with 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

    5. Examples

    6. Complex Numbers A complex number has a real part & an imaginary part. Standard form is:

    7. The Complex plane

    8. Graphing in the complex plane

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

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

    12. 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:

    13. Examples 1.

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