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manjuthottam
 2 years ago
COMPLEX VARIABLES: Can someone explain how to find the Arg z and what does it mean?
manjuthottam
 2 years ago
COMPLEX VARIABLES: Can someone explain how to find the Arg z and what does it mean?

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

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

manjuthottam
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359087681895:dw

joemath314159
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1oh so r = modulus of the point (a,b)?

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

joemath314159
 2 years 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
 2 years 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
 2 years 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
 2 years 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
 2 years 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
 2 years 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
 2 years 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
 2 years 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
 2 years 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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