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Sinz

  • 3 years ago

Simplify the following quotient of complex numbers into the form a + bi. -9+8i/1+2i

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  1. Walleye
    • 3 years ago
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    You going to mutiply the numorator and the denominatior by the conjugate. Does that help?

  2. Sinz
    • 3 years ago
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    so multiply -9 and 1 right

  3. jimmyrep
    • 3 years ago
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    multiply top and bottom of the quotient by the conjugate of 1 + 2i which is 1 - 2i

  4. Sinz
    • 3 years ago
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    huh I am confused

  5. Walleye
    • 3 years ago
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    Your goal here is to "kill" the bottom complex number. you can do this by \[(9+8i/1+2i) * (1 - 2i / 1 - 2i)\] remember that 1-2i / 1-2i = 1 and you can multiply anything by 1

  6. Walleye
    • 3 years ago
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    without changing the number

  7. Sinz
    • 3 years ago
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    okay

  8. jimmyrep
    • 3 years ago
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    (-9 + 8i)(1-2i) ------------ (1+2i)(1-2i) the denominator simplifies to 1 + 4 = 5

  9. Sinz
    • 3 years ago
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    so I take and combine like terms right?

  10. Walleye
    • 3 years ago
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    yep. you'll find that if you multiply a complex number by its conjugate then you kill all of the i terms and just be left with real numbers

  11. Sinz
    • 3 years ago
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    after I get the )-9+8i)(1-2i)

  12. Sinz
    • 3 years ago
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    so it will be -9*1 and 8i*-2i?

  13. jimmyrep
    • 3 years ago
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    yes - u now simplify the top expression then divide by 5

  14. jimmyrep
    • 3 years ago
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    no remember (a+b)(a+b) = a^2 + 2ab + b^2

  15. Sinz
    • 3 years ago
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    so -9 - 16i/5 is what it should look like right

  16. Walleye
    • 3 years ago
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    nope. your top term is off. Try using FOIL on the top again and see if you get somthing else.

  17. Sinz
    • 3 years ago
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    okay lemme see (-9+8i)(1-2i) combine like terms -9*1=-9 8i*2i=16i total is -9+16i/5 is that right

  18. jimmyrep
    • 3 years ago
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    (-9 + 8i)(1-2i) = -9 + 18i + 8i + 16 = 7 + 26i the second bracket is first multiplied by -9 then its multuplied by + 81

  19. jimmyrep
    • 3 years ago
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    by +8i

  20. Sinz
    • 3 years ago
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    oh okay wasn't seeing how it was done that is why I was confuzzled

  21. Walleye
    • 3 years ago
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    I dont know if this will help but treat i just like you would x when your distributing! I find that thinking about it that way very helpfful

  22. jimmyrep
    • 3 years ago
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    final result is 7/5 + (26/5) i

  23. Sinz
    • 3 years ago
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    okay so in algebra they try to change things up so it confuses you?

  24. Sinz
    • 3 years ago
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    Thank you Jimmy you was very helpful as was you Walleye

  25. Walleye
    • 3 years ago
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    yw!

  26. jimmyrep
    • 3 years ago
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    thats ok

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