Convert complex number to Polar form | Mathematics | Page 1

mellow oar Jan 31, 2024, 4:49 AM

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I have the recatngualr complex number $-\sqrt{3} - i$ I have that $|z| = 2$ and we get that $z = 2( -\sqrt{3}/2 - i/2)$

Now we know that the angle x should have the property that $cos(x) = \frac{\sqrt{3}}{2}$ and $sin(x) = \frac{-1}{2}$ however not only do I get two different angles, the anwsers I got namely pi/6 and -pi/6 respectively is wrong , the anwser key says the answer is the angle is -5pi/6. What am I doing wrong here?

tired valeBOT Jan 31, 2024, 4:49 AM

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slow sluiceBOT Jan 31, 2024, 4:53 AM

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jayz

deft knoll Jan 31, 2024, 4:58 AM

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your complex number is in the 3rd quadrant

mellow oar Jan 31, 2024, 5:12 AM

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deft knoll your complex number is in the 3rd quadrant

Yes so how did I manage to get pi/6 and -pi/6?

deft knoll Jan 31, 2024, 5:14 AM

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oops fixed my mistake but

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i believe you just did arccos(sqrt(3)/2) and arcsin(-1/2)

mellow oar Jan 31, 2024, 5:14 AM

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yeah

deft knoll Jan 31, 2024, 5:15 AM

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yes

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thats how you got your answer

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hmm actually thats weird

mellow oar Jan 31, 2024, 5:15 AM

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right but the actual correct anwser is -5pi/6

deft knoll Jan 31, 2024, 5:15 AM

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im not sure why cosine is positive

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cos x = -sqrt(3)/2

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can you post the full question?

mellow oar Jan 31, 2024, 5:17 AM

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sure.

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deft knoll Jan 31, 2024, 5:18 AM

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ok so

mellow oar Jan 31, 2024, 5:18 AM

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deft knoll Jan 31, 2024, 5:18 AM

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if you cant visualize it, did you draw this out as a triangle?

mellow oar Jan 31, 2024, 5:18 AM

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yeah

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I did

deft knoll Jan 31, 2024, 5:18 AM

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yeah your answer key is correct then

mellow oar Jan 31, 2024, 5:18 AM

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how though?

deft knoll Jan 31, 2024, 5:19 AM

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we know the modulus of z is 2
i dont need to show that, right?

mellow oar Jan 31, 2024, 5:19 AM

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yup

deft knoll Jan 31, 2024, 5:19 AM

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ok

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if we draw the triangle in the third quadrant

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and we know its in the third quadrant because both the real part and the imaginary part of z are negative

mellow oar Jan 31, 2024, 5:19 AM

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yup I did that

deft knoll Jan 31, 2024, 5:23 AM

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well

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i was typing something up in ms paint and it got cut off

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its better to write it as -5pi/6 because the function w(z) = Arg(z) means the range is [-pi, pi]

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we do + 2 pi k (where k is an integer) to show every revolution around the circle

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however 7pi/6 is acceptable, that's not wrong

mellow oar Jan 31, 2024, 5:26 AM

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Ok I see perfect thanks 🙂

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is there any faster way of trying to find theta

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drawing a diagram and figuring this out seems like a hassle

deft knoll Jan 31, 2024, 5:27 AM

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ummm

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if you are familiar enough with it then you can intuitively figure it out

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that's how it was for me at least

mellow oar Jan 31, 2024, 5:27 AM

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i see fair enough

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thanks

deft knoll Jan 31, 2024, 5:27 AM

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did you learn about the

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special right triangles?

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i think that's what they're called

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45-45-90 and 30-60-90

mellow oar Jan 31, 2024, 5:28 AM

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no never heard of it

deft knoll Jan 31, 2024, 5:28 AM

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ah ok

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alright best of luck with the rest of your work then

tired valeBOT Feb 10, 2024, 3:53 PM

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mellow oar I have the recatngualr complex number $-\sqrt{3} - i$ I have that $|z| = 2$ and ...

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mellow oar Feb 17, 2024, 12:34 AM

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#Convert complex number to Polar form