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Math Help - Finding complex number from polar coordinates

  1. #1
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    Finding complex number from polar coordinates

    Thanks for all the help on the previous problems, I figured out all my problems! Now, I'm stuck on another kinda simple area. Converting polar coordinates to complex numbers...

    Give the complex number whose polar coordinates (r,\theta) are

    (a) (\sqrt{3},\frac{\pi}{4})

    (b)  (4, \frac{-\pi}{2})

    If someone could just walk me through one of the problems, I would greatly appreciate it! I have 6 of these to do, and I'm pretty sure I can figure them all out if someone can provide me with a walk-through on one! Thanks, and good night! zzzz
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    Moo
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    Hi !

    It's just z=r \cdot e^{i \theta}=r \cdot (\cos(\theta)+i \sin(\theta))



    Why ?
    Because r represents the distance from the origin to the point, which corresponds to the modulus you know \sqrt{x^2+y^2}. Make a sketch, you will understand !
    For the angles, it's the same, look at a sketch.
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    Is the answer to (a)  \sqrt{2} + \sqrt{2}i ?
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    Thanks Moo, I actually used that to figure out my answer before looking at your post! I think it is correct... Q_Q
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    How did you find \sqrt{2} + \sqrt{2}i ?

    r\cdot (\cos \theta + i \sin \theta ) = \sqrt{3}\cdot (\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}) = \frac{\sqrt{6}}{2}+\frac{\sqrt{6}}{2}i
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    Very sleepy and dumb mistake. I see now, thanks.
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  7. #7
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    Quote Originally Posted by shadow_2145 View Post
    Thanks for all the help on the previous problems, I figured out all my problems! Now, I'm stuck on another kinda simple area. Converting polar coordinates to complex numbers...

    Give the complex number whose polar coordinates (r,\theta) are

    (a) (\sqrt{3},\frac{\pi}{4})

    (b)  (4, \frac{-\pi}{2})

    If someone could just walk me through one of the problems, I would greatly appreciate it! I have 6 of these to do, and I'm pretty sure I can figure them all out if someone can provide me with a walk-through on one! Thanks, and good night! zzzz
    For the second, you'd get z=4(\cos(\frac{-\pi}{2})+i \sin(\frac{-\pi}{2}))=4(0-i)=-4i
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