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very simple complex numbers thought (1 Viewer)

Rahul

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ever wondered how the modulus of a comlex number is found, not the application of the formula, but the actual derivation of it?

this may be stupid for u, but i jus found it out today...lol

does anyone know it?
 

McLake

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Do you mean the fact that it is the distance that it is from the origin on the Argand Plane?
 

Rahul

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yes, but if u were given a diagram with axis, and a complex number z, how would u work out |z|.

i'm probably not explaining the question properly...its simple really. a diagram i have may show u what i mean, but it would give it away....get ppl thinking
 

Affinity

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You're not alluding to one of our greek friend's work are you.
 

Toodulu

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i didn't realise there was a formula for finding |z|, i just work it out?
 

Affinity

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yes, but if u were given a diagram with axis, and a complex number z, how would u work out |z|.
Measure with a ruler or for accuracy, use a micrometer gauge.
 

underthesun

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im not too sure, but |z| means distance right?

then, if you're not calculating that using modulus, you do this

let z = x+iy

|z| = |x+iy| = |x - iy|

then, |z|<sup>2</sup> = |x+iy||x-iy|
= |x<sup>2</sup> + y<sup>2</sup>| .....(1)
then the number could be added, and then square root that expression (1).
 

deepulse

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let z = x + iy

plotting it, you get the point (x,y)

and we know |z| = distance from origine to end of the vector thingy

so drawing a triangle

<pre> /|
/ |
/ |</pre>

(its supposed to look like a triangle, but it doesnt~!) :p

where the height is y
and base is x
and the bottom left corner is O

so |z| (or the hypotenuse) = sqrt ( x^2 + y^2) from pythagorus
 

Rahul

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yep thats it underthesun and deepulse.

i never used to think of it as a right angled triangle, i jus applied the sqroot(x^2 + y^2)

good to know where formulas come from rather than applying it each time.

Originally posted by underthesun

let z = x+iy

|z| = |x+iy| = |x - iy|

then, |z|<sup>2</sup> = |x+iy||x-iy|
= |x<sup>2</sup> + y<sup>2</sup>|
i never thought of it that way:). i learnt something:D:D
 

Newbie

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i just use a ruler hmmm no wonder im getting consistently <70% in exams :(
 

Rahul

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Originally posted by VanCarBus
| z | = distance = real squared + i's value squared
its sqrt(real squared + i's value squared) :)


Originally posted by underthesun
pfft you should have given me a discount for that geha book then :)

say.. $5? :D
errr....i'll get back to you;)
 

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