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JenniferSmart1

  • 2 years ago

How do I find absolute values of complex numbers? |7-i|

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  1. satellite73
    • 2 years ago
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    pythatgoras \[|a+bi|=\sqrt{a^2+b^2}\]

  2. satellite73
    • 2 years ago
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    *pythagoras

  3. satellite73
    • 2 years ago
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    in your case \(a=7,b=-1\) so you can just about do it in your head

  4. satellite73
    • 2 years ago
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    \[\sqrt{7^2+1^2}=\sqrt{491}=\sqrt{50}=5\sqrt2\]

  5. satellite73
    • 2 years ago
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    not much to memorize, the hypotenuse is the square root of the sum of the squares, as in a right triangle

  6. JenniferSmart1
    • 2 years ago
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    but what has an "i" to do with a triangle?

  7. satellite73
    • 2 years ago
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    |dw:1358396646228:dw|

  8. satellite73
    • 2 years ago
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    the complex numbers live in the complex plane the absolute value is the distance from the origin, which you get via pythagoras \[a^2+b^2=h^2\] \[h=\sqrt{a^2+b^2}\]

  9. JenniferSmart1
    • 2 years ago
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    is the triangle always in that quadrant?

  10. Callisto
    • 2 years ago
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    No, it depends on the complex number. Let a, b = +ve a+bi => quad. I -a + bi => quad. II -a - bi => quad. III a - bi => quad. IV

  11. JenniferSmart1
    • 2 years ago
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    ahh good to know...so is "a" and "b" the length of the lines?

  12. satellite73
    • 2 years ago
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    it doesn't make any difference however, what quadrant you are in, it is still \[|a+bi|=\sqrt{a^2+b^2}\] i just put it there because your number was \(7-i\)

  13. satellite73
    • 2 years ago
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    |dw:1358397280980:dw|

  14. Callisto
    • 2 years ago
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    |dw:1358397320522:dw|

  15. JenniferSmart1
    • 2 years ago
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    That makes sense...I just have one more dumb question a+bi....is that the location of the point at the end of that line?

  16. JenniferSmart1
    • 2 years ago
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    oh no that is the length of the line....durrr..sorry!!!1

  17. JenniferSmart1
    • 2 years ago
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    the absolute value of a+bi is the length of the line...correct?

  18. Callisto
    • 2 years ago
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    a + bi a = number (coordinate) in the real part b = number (coordinate) in the imaginary part | a+bi | = length of the line => yes, I think (Actually... I haven't learnt it in the lesson yet.. So...)

  19. JenniferSmart1
    • 2 years ago
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    that's cool...It makes sense to me though. Thanks soo much @Callisto =)

  20. satellite73
    • 2 years ago
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    yes, it is the length of the line, that is, the distance between the complex number \(a+bi\) and the origin

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