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 one year ago
COMPLEX VARIABLES: Can someone explain how to find the Arg z and what does it mean?
 one year ago
COMPLEX VARIABLES: Can someone explain how to find the Arg z and what does it mean?

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joemath314159
 one year ago
Best ResponseYou've already chosen the best response.1If I give you a complex number in \[a+bi\]form, do you know how to convert it to its "polar" form\[re^{i\theta}\]?

joemath314159
 one year ago
Best ResponseYou've already chosen the best response.1Because when written in its polar form:\[\arg(re^{i\theta})=\theta\]

manjuthottam
 one year ago
Best ResponseYou've already chosen the best response.1where does a and b go?

manjuthottam
 one year ago
Best ResponseYou've already chosen the best response.1I don't know how to convert it to its polar form, could you help me understand that formula?

joemath314159
 one year ago
Best ResponseYou've already chosen the best response.1dw:1359087681895:dw

joemath314159
 one year ago
Best ResponseYou've already chosen the best response.1r is the length of the complex number, given by using pythagorean theorem:\[r=\sqrt{a^2+b^2}\]

joemath314159
 one year ago
Best ResponseYou've already chosen the best response.1the angle is the argument. You use inverse tangent to get it.\[\theta=\tan ^{1}(\frac{a}{b})\]

manjuthottam
 one year ago
Best ResponseYou've already chosen the best response.1oh so r = modulus of the point (a,b)?

manjuthottam
 one year ago
Best ResponseYou've already chosen the best response.1so when asked arg z, it is the theta that they are asking for?

joemath314159
 one year ago
Best ResponseYou've already chosen the best response.1yes, they want the angle. Be careful when using that formula though. You need to make sure the answer you get reflects the right quadrant. Ex. arg(1+i) vs. arg(1i)

manjuthottam
 one year ago
Best ResponseYou've already chosen the best response.1so when asked the arg of 1st quadrant, theta is by the formula you gave me; when asked the arg of quadrant 3, theta is tan inverse of (b/a) ?

joemath314159
 one year ago
Best ResponseYou've already chosen the best response.1ack! thanks for pointing out my mistake, it should be b/a in the formula i posted.

joemath314159
 one year ago
Best ResponseYou've already chosen the best response.1the problem arises because inverse tangent always gives an angle between pi/2 and pi/2, but you want an angle between 0 and 2pi. So if you were asked for the argument of 1i, the formula would give pi/4 as an answer, but you know you want something in the 3rd quadrant, so you add pi to get the correct answer of 5\pi/4

manjuthottam
 one year ago
Best ResponseYou've already chosen the best response.1oh ok that makes sense! Thanks!! may i ask another question related? How do i put it into the form of Re^(i theta)? actually what is that formula mean? is it just the form of the vector?

manjuthottam
 one year ago
Best ResponseYou've already chosen the best response.1i understand how to get r and theta now, but i was wondering if it is a vector and why is there the 'e'?

joemath314159
 one year ago
Best ResponseYou've already chosen the best response.1Once you know the modulus and argument of a complex number, you know what r and theta are. Euler's formula says:\[e^{i\theta}=\cos\theta+i\sin\theta\]

joemath314159
 one year ago
Best ResponseYou've already chosen the best response.1Note that the modulus of e^(itheta)=1 since:\[\cos\theta+i\sin\theta=\cos ^2\theta+\sin^2\theta=1\]So the polar form of a complex number\[re^{i\theta}\]it really just saying, "i want a complex number whose length is r, in the direction of theta"

manjuthottam
 one year ago
Best ResponseYou've already chosen the best response.1oh i get it now!! I really appreciate you helping me!! Thank you so much!!
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