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Mastering Complex Numbers: Application and Simplification Techniques

Learn how to apply imaginary numbers in solving complex number problems and combine complex numbers. Practice addition, subtraction, and multiplication of complex numbers with step-by-step examples included.

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Mastering Complex Numbers: Application and Simplification Techniques

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  1. 5.7.2 – Complex Numbers

  2. From yesterday, we learned the application of the imaginary unit i • Used for problems such as; • -5x2 = 20

  3. Complex Number • As part of the imaginary numbers and the imaginary number system, we have what are known as Complex Numbers • What does the word complex mean? • a + bi • a = real number • bi = imaginary number

  4. Combining Complex Numbers • Similar to like variables (2x, 10x, -x) and like powers (x4, 10x4), we may combine line terms from complex numbers • To add or subtract complex numbers, we do the following • 1) Combine the real parts with real parts • 2) Combine the imaginary parts with imaginary parts

  5. Example. Simplify the following expressions • 1) (2 + 5i) + (3 + 10i) • 2) (-9 – 4i) + 10i • 3) -13i – (4 + 6i) • 4) 19i – 5i + 2

  6. Multiplication • With multiplication, we will treat them as a previous problem we have already done • What does the problem (2 + 5i)(1 + i) resemble? • Is there a previous method we can use to help us?

  7. May use “FOIL” or the punnett square method • Example. Find the product of the two complex numbers; (2 + 5i)(1 + i)

  8. Example. Find the product of the two complex numbers; • (3 -2i)(3 + 2i)

  9. Example. Find the product of the two complex numbers; • (-4 -i)(-4 + 4i)

  10. Example. Find the product of the two complex numbers; • (i + 3)2

  11. Complete the following problems with your neighbors. We will check answers in 5 minutes. • Simplify each of the following expressions. • 1) 2 + 4i + 17 – 6i • 2) (9 + 7i) – (4 – 5i) • 3) (2 + i)(7 – 3i) • 4) (6 + 2i)(1 + 2i)

  12. Assignment • Pg. 265 • 27 – 49 odd

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