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JenniferSmart1
 3 years ago
How do I find absolute values of complex numbers?
7i
JenniferSmart1
 3 years ago
How do I find absolute values of complex numbers? 7i

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satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3pythatgoras \[a+bi=\sqrt{a^2+b^2}\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3in your case \(a=7,b=1\) so you can just about do it in your head

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3\[\sqrt{7^2+1^2}=\sqrt{491}=\sqrt{50}=5\sqrt2\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3not much to memorize, the hypotenuse is the square root of the sum of the squares, as in a right triangle

JenniferSmart1
 3 years ago
Best ResponseYou've already chosen the best response.0but what has an "i" to do with a triangle?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3dw:1358396646228:dw

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3the complex numbers live in the complex plane the absolute value is the distance from the origin, which you get via pythagoras \[a^2+b^2=h^2\] \[h=\sqrt{a^2+b^2}\]

JenniferSmart1
 3 years ago
Best ResponseYou've already chosen the best response.0is the triangle always in that quadrant?

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.2No, 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

JenniferSmart1
 3 years ago
Best ResponseYou've already chosen the best response.0ahh good to know...so is "a" and "b" the length of the lines?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3it 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 \(7i\)

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3dw:1358397280980:dw

JenniferSmart1
 3 years ago
Best ResponseYou've already chosen the best response.0That makes sense...I just have one more dumb question a+bi....is that the location of the point at the end of that line?

JenniferSmart1
 3 years ago
Best ResponseYou've already chosen the best response.0oh no that is the length of the line....durrr..sorry!!!1

JenniferSmart1
 3 years ago
Best ResponseYou've already chosen the best response.0the absolute value of a+bi is the length of the line...correct?

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.2a + 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...)

JenniferSmart1
 3 years ago
Best ResponseYou've already chosen the best response.0that's cool...It makes sense to me though. Thanks soo much @Callisto =)

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3yes, it is the length of the line, that is, the distance between the complex number \(a+bi\) and the origin
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